/matlabcentral/discussions/channelsディスカッション Channels 件2024-11-05T13:58:51Ztag:jp.mathworks.com,2005:Topic/8764222024-10-21T14:04:01Z2024-10-21T14:04:01ZWelcome to the MATLAB & Simulink Book Discussion Channel! <p>Hello! The MathWorks Book Program is thrilled to welcome you to our discussion channel dedicated to books on MATLAB and Simulink. Here, you can:
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We’re excited to see the discussions and exchanges that will unfold here. Whether you're an expert or beginner, there's a place for you in our community. Let's embark on this journey together!</p>Book Programhttps://jp.mathworks.com/matlabcentral/profile/authors/35489698tag:jp.mathworks.com,2005:Topic/8648412024-06-03T21:22:40Z2024-10-01T10:01:07ZWelcome to the Cody Discussion Channel! Please Read Before Posting<p>Hello and a warm welcome to everyone! We're excited to have you in the Cody Discussion Channel. To ensure the best possible experience for everyone, it's important to understand the types of content that are most suitable for this channel.</p><p>Content that belongs in the Cody Discussion Channel:
Tips & tricks: Discuss strategies for solving Cody problems that you've found effective.
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General discussions: Anything else related to Cody that doesn't fit into the above categories.</p><p>Content that does not belong in the Cody Discussion Channel:
Comments on specific Cody problems: Examples include unclear problem descriptions or incorrect testing suites.
Comments on specific Cody solutions: For example, you find a solution creative or helpful.
Please direct such comments to the Comments section on the problem or solution page itself.</p><p>We hope the Cody discussion channel becomes a vibrant space for sharing expertise, learning new skills, and connecting with others.</p>Chen Linhttps://jp.mathworks.com/matlabcentral/profile/authors/6682740tag:jp.mathworks.com,2005:Topic/8723812024-07-31T20:34:15Z2024-09-23T07:43:17ZUsing MATLAB to find a generative equation for a sequence<p>This stems purely from some play on my part. Suppose I asked you to work with the sequence formed as 2*n*F_n + 1, where F_n is the n'th Fibonacci number? Part of me would not be surprised to find there is nothing simple we could do. But, then it costs nothing to try, to see where MATLAB can take me in an explorative sense.
n = sym(0:100).';
Fn = fibonacci(n);
Sn = 2*n.*Fn + 1;
Sn(1:10) % A few elements
For kicks, I tried asking ChatGPT. Giving it nothing more than the first 20 members of thse sequence as integers, it decided this is a Perrin sequence, and gave me a recurrence relation, but one that is in fact incorrect. Good effort from the Ai, but a fail in the end.
Is there anything I can do? Try null! (Look carefully at the array generated by Toeplitz. It is at least a pretty way to generate the matrix I needed.)
X = toeplitz(Sn,[1,zeros(1,4)]);
rank(X(5:end,:))
Hmm. So there is no linear combination of those columns that yields all zeros, since the resulting matrix was full rank.
X = toeplitz(Sn,[1,zeros(1,5)]);
rank(X(6:end,:))
But if I take it one step further, we see the above matrix is now rank deficient. What does that tell me? It says there is some simple linear combination of the columns of X(6:end,:) that always yields zero. The previous test tells me there is no shorter constant coefficient recurrence releation, using fewer terms.
null(X(6:end,:))
Let me explain what those coefficients tell me. In fact, they yield a very nice recurrence relation for the sequence S_n, not unlike the original Fibonacci sequence it was based upon.
S(n+1) = 3*S(n) - S_(n-1) - 3*S(n-2) + S(n-3) + S(n-4)
where the first 5 members of that sequence are given as [1 3 5 13 25]. So a 6 term linear constant coefficient recurrence relation. If it reminds you of the generating relation for the Fibonacci sequence, that is good, because it should. (Remember I started the sequence at n==0, IF you decide to test it out.) We can test it out, like this:
SfunM = memoize(@(N) Sfun(N));
SfunM(25)
2*25*fibonacci(sym(25)) + 1
And indeed, it works as expected.
function Sn = Sfun(n)
switch n
case 0
Sn = 1;
case 1
Sn = 3;
case 2
Sn = 5;
case 3
Sn = 13;
case 4
Sn = 25;
otherwise
Sn = Sfun(n-5) + Sfun(n-4) - 3*Sfun(n-3) - Sfun(n-2) +3*Sfun(n-1);
end
end
A beauty of this, is I started from nothing but a sequence of integers, derived from an expression where I had no rational expectation of finding a formula, and out drops something pretty. I might call this explorational mathematics.
The next step of course is to go in the other direction. That is, given the derived recurrence relation, if I substitute the formula for S_n in terms of the Fibonacci numbers, can I prove it is valid in general? (Yes.) After all, without some proof, it may fail for n larger than 100. (I'm not sure how much I can cram into a single discussion, so I'll stop at this point for now. If I see interest in the ideas here, I can proceed further. For example, what was I doing with that sequence in the first place? And of course, can I prove the relation is valid? Can I do so using MATLAB?)
(I'll be honest, starting from scratch, I'm not sure it would have been obvious to find that relation, so null was hugely useful here.)</p>John D'Erricohttps://jp.mathworks.com/matlabcentral/profile/authors/869215tag:jp.mathworks.com,2005:Topic/8441012024-02-02T17:41:51Z2024-07-15T14:56:50ZRead this before posting<p>Hello and a warm welcome to all! We're thrilled to have you visit our community. MATLAB Central is a place for learning, sharing, and connecting with others who share your passion for MATLAB and Simulink. To ensure you have the best experience, here are some tips to get you started:
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Enjoy yourself and have fun! We're committed to fostering a supportive and educational environment. Dive into discussions, share your expertise, and grow your knowledge. We're excited to see what you'll contribute to the community!</p>Davidhttps://jp.mathworks.com/matlabcentral/profile/authors/4480925tag:jp.mathworks.com,2005:Topic/8768972024-11-05T13:44:42Z2024-11-05T13:58:51ZMATLAB is looking forward to having an intelligent AI programming assistant similar to GitHub Copilot<p>In the past two years, large language models have brought us significant changes, leading to the emergence of programming tools such as GitHub Copilot, Tabnine, Kite, CodeGPT, Replit, Cursor, and many others. Most of these tools support code writing by providing auto-completion, prompts, and suggestions, and they can be easily integrated with various IDEs.
As far as I know, aside from the MATLAB-VSCode/MatGPT plugin, MATLAB lacks such AI assistant plugins for its native MATLAB-Desktop, although it can leverage other third-party plugins for intelligent programming assistance. There is hope for a native tool of this kind to be built-in.</p>cui,xingxinghttps://jp.mathworks.com/matlabcentral/profile/authors/3388605tag:jp.mathworks.com,2005:Topic/8768842024-11-05T01:48:23Z2024-11-05T13:44:59Zthe MATLAB Shorts Mini Hack contest<p>Mini Hack is brilliant！Let's use MATLAB to create the future!</p>Tianyihttps://jp.mathworks.com/matlabcentral/profile/authors/28184748tag:jp.mathworks.com,2005:Topic/8760472024-10-09T18:54:26Z2024-11-05T09:02:40ZWhat would you ask the MATLAB leadership team?<p>Let's say you have a chance to ask the MATLAB leadership team any question. What would you ask them?</p>Hans Scharlerhttps://jp.mathworks.com/matlabcentral/profile/authors/5863695tag:jp.mathworks.com,2005:Topic/8667112024-06-18T21:19:39Z2024-11-05T01:28:37ZAsk Me Anything about image analysis or the Mathworks community<p>Hello, everyone! I’m Mark Hayworth, but you might know me better in the community as Image Analyst. I've been using MATLAB since 2006 (18 years). My background spans a rich career as a former senior scientist and inventor at The Procter & Gamble Company (HQ in Cincinnati). I hold both master’s & Ph.D. degrees in optical sciences from the College of Optical Sciences at the University of Arizona, specializing in imaging, image processing, and image analysis. I have 40+ years of military, academic, and industrial experience with image analysis programming and algorithm development. I have experience designing custom light booths and other imaging systems. I also work with color and monochrome imaging, video analysis, thermal, ultraviolet, hyperspectral, CT, MRI, radiography, profilometry, microscopy, NIR, and Raman spectroscopy, etc. on a huge variety of subjects.
I'm thrilled to participate in MATLAB Central's Ask Me Anything (AMA) session, a fantastic platform for knowledge sharing and community engagement. Following Adam Danz’s insightful AMA on staff contributors in the Answers forum, I’d like to discuss topics in the area of image analysis and processing. I invite you to ask me anything related to this field, whether you're seeking recommendations on tools, looking for tips and tricks, my background, or career development advice. Additionally, I'm more than willing to share insights from my experiences in the MATLAB Answers community, File Exchange, and my role as a member of the Community Advisory Board. If you have questions related to your specific images or your custom MATLAB code though, I'll invite you to ask those in the Answers forum. It's a more appropriate forum for those kinds of questions, plus you can get the benefit of other experts offering their solutions in addition to me.
For the coming weeks, I'll be here to engage with your questions and help shed light on any topics you're curious about.</p>Image Analysthttps://jp.mathworks.com/matlabcentral/profile/authors/1343420tag:jp.mathworks.com,2005:Topic/8768592024-11-04T12:57:20Z2024-11-04T23:15:55ZMATLAB's Fractal Art<pre> At the onset of each week, I release a post that analyzes code with the intent of making it accessible for beginners, while also providing insights that can benefit more experienced users seeking to learn new techniques or approaches.
This week, my inspiration comes from the fractal art produced in MATLAB, as presented in my entry Whispers of the Ocean's Breeze:</pre><pre> Below, I offer a pretty detailed walkthrough of the code break-down, with the goal of creating both an educational and stimulating experience for those eager to learn or find some inspiration. Taking into account that this post is somewhat lengthy, it provides a breakdown and summary of various techniques. It is my hope that it will assist someone and allow readers to focus on the sections that are of most interest to them.
While the code contains comments, this post offers additional explanations and details.</pre><p>1. Function Definition and Metadata</p><p>function drawframe(f)
Line 1: Defines the main function drawframe, which takes a single parameter f. This parameter controls various aspects of the animation, such as movement or speed.</p><p>% Audio source: Klapa Šibenik (comp. Arsen Dedić) -
% - Zaludu me svitovala mati
% (Hrvatska 🇭🇷, (Dalmacija))</p><p>% Enhanced aesthetics and added dynamic movement,
% offering a creative Remix of my earlier concept.
% (This version brings richer visual appeal,smoother transitions,
% and a more engaging animation flow)
Lines 2-4: Commented-out lines providing metadata or notes about the code. These comments describe the aesthetic goals and improvements in this version, highlighting that it's a remix of one of my earlier entry's, with added dynamic movement and smoother visuals. (These notes are not executed by MATLAB.)
A general tip for using comments: include comments in your code as frequently as needed. They serve as helpful reminders of what each part of the code does, especially when you revisit it after some time, and make it easier for others who may read or use your code.</p><p>2. Function Call to seaweed</p><p>seaweed(4) % The value in brackets can be adjusted for significantly
% enhanced visualization,
% but it exceeds the 235-second limit in the contest script.
% Feel free to experiment at Desktop workstation - with higher
% values in the loop,
% for more complex and beautiful results.
Line 5: Calls the seaweed function with an argument of 4. The number 4 controls the recursion depth, affecting how detailed or complex the 'seaweed' pattern will be.
Lines 6-9: Comment explaining that increasing the value in seaweed(4) enhances visualization but may exceed time limits in contest environment(s). This suggests adjusting this parameter on a desktop to explore more intricate patterns...</p><p>3. Definition of seaweed Function</p><p>function seaweed(k)
% Set up the figure window with a specific position and background color
figure('Position', [60+2*f, 60-2*f, 600, 600], 'Color', [0.15, 0.15, 0.5]);
Line 10: Defines the seaweed function, which takes a parameter k (depth of recursion). This function initializes the graphical figure window.
Line 12: Sets up the figure window with a position influenced by f, making the figure’s position change dynamically with f. The background color [0.15, 0.15, 0.5] creates a dark blue background, enhancing the underwater aesthetic.</p><p>4. Recursive Drawing with crta Function</p><pre> crta([0, 0], 90, k, k);</pre><pre> % Make the axes equal and turn them off for a clean figure
axis equal
axis off
Line 14: Calls the recursive function crta, starting the drawing process at [0, 0](origin point) with a 90-degree angle. Both k values set the initial recursion depth and maximum recursion level.
Lines 16-17: Sets the axis scale to equal, ensuring no distortion, and turns off the axes for a cleaner display.</pre><p>5. Definition of crtaFunction and Initialization of Parameters</p><pre> function crta(tck, ugao, prstiter, r)
% Define thickness of line segment proportional to current depth
sir = 5 * (prstiter / r);
% Define length of the line segment
duz1 = 5 * prstiter;
Line 18: Defines crta, a nested function within seaweed, taking parameters tck (current coordinates), ugao (angle), prstiter (current recursion depth), and r (maximum recursion depth).
Lines 20-21: Defines sir (line thickness) to be proportional to the current recursion depth, prstiter, creating thinner branches as depth increases. While, duz1 defines the line segment length, which shortens with each recursion, creating perspective.</pre><p>6. Angle Calculations for Branching</p><pre> % Define four branching angles with slight variations
ug1 = ugao + 15 + (f / 15);
ug2 = ugao + 7 - f / 15;
ug3 = ugao - 7 + f / 15;
ug4 = ugao - 15 - f / 15;
Lines 23-27: Sets branching angles ug1, ug2, ug3, and ug4 relative to the initial angle ugao, adding and subtracting small amounts. These angles, influenced by f, introduce subtle variations, enhancing the natural appearance.</pre><p>7. Calculations for Branch Endpoints</p><pre> % Calculate endpoints of each line segment for the four angles
a1 = duz1 * sind(ug1) + tck(2);
b1 = duz1 * cosd(ug1) + tck(1);
c2 = duz1 * sind(ug2) + tck(2);
a2 = duz1 * cosd(ug2) + tck(1);
b3 = duz1 * sind(ug3) + tck(2);
c3 = duz1 * cosd(ug3) + tck(1);
d4 = duz1 * sind(ug4) + tck(2);
e4 = duz1 * cosd(ug4) + tck(1);
Lines 29-36: Calculates x and y endpoints for each of the four branches using sind and cosd functions, which convert angles into coordinates. Each branch starts at tck(current In this section, the code calculates the endpoints of four line segments, each corresponding to a distinct angle (ug1, ug2,ug3, and ug4). These endpoints are computed based on the length of the line segment duz1, which scales with recursion depth to make each segment shorter as the recursive function progresses. The trigonometric functions sind and cosd are used here to calculate the horizontal and vertical displacements of each segment relative to the current position, tck. While, sind and cosd functions compute the sine and cosine of each angle in degrees, returning the y and x displacements, respectively. For each angle, multiplying by duz1scales these displacements to achieve the intended length for each line segment. Each endpoint coordinate is calculated by adding these displacements to the initial position, tck, to determine the final position for each branch segment:
a1 and b1 represent the y and x endpoints for the segment at angle ug1
c2 and a2 represent the y and x endpoints for the segment at angle ug2
b3 and c3 represent the y and x endpoints for the segment at angle ug3
d4 and e4 represent the y and x endpoints for the segment at angle ug4
These coordinates form the four main branches radiating out from the current position in different directions. By varying the angle slightly for each branch and scaling the length proportionally, the function generates a visually rich, organic branching structure that resembles seaweed or other natural patterns.</pre><p>8. Midpoint Calculations for Additional Complexity</p><pre> % Calculate midpoints for additional "leaves" to
% simulate complexity
uga1 = ug2 - 5 + f / 5;
ugb2 = ug3 + 5 - f / 5;
uga2 = duz1 / 2 * sind(uga1) + c2 + f / 20;
ugb3 = duz1 / 2 * cosd(uga1) + a2 - f / 20;
ugc2 = duz1 / 2 * sind(ugb2) + b3 + f / 20;
ugda1 = duz1 / 2 * cosd(ugb2) + c3 - f / 20;
Lines 38-44: Calculates midpoint angles and positions for extra “leaf” structures. This further enhances the fractal appearance by adding more detail, as these points fall between main branches!
Additional midpoints are calculated to add further detail and complexity to the fractal pattern. These midpoints represent extra branches or “leaves” that emerge from within the main branch segments, enhancing the natural, organic appearance of the fractal structure. Consequently, uga1 and ugb2 are new angles derived by slightly modifying the main branch angles ug2and ug3. The adjustments are made by adding and subtracting small values, including a component based on f. These subtle variations create slight deviations in the angles of the additional branches, making them appear more random and organic, like leaves growing off main stems in varied directions. Once the new angles uga1 and ugb2 are defined, they are used to calculate intermediate coordinates along the main branch lines. These midpoints are positioned halfway along each branch segment, representing the location from which the extra “leaf” branches will emerge.
To find these midpoints:
uga2 and ugb3 use sind(uga1) and cosd(uga1)to calculate the y and x coordinates halfway along the segment for angle ug2.
ugc2 and ugda1 similarly use sind(ugb2) and cosd(ugb2) to get the coordinates for angle ug3.
Each midpoint calculation also includes a slight additional offset based on f (like f / 20), adding variation in their positions and contributing to the irregular, natural look of the structure.
By adding these secondary branches, the fractal pattern gains more intricacy. These “leaves” give a more complex and dense appearance, resembling the growth patterns of plants or seaweed where smaller branches diverge from main stems. The addition of midpoints also contributes to the overall depth and richness of the fractal design, ensuring that each recursive call doesn’t simply repeat but also grows in visual detail, making the resulting fractal more visually appealing and realistic. The midpoint calculations thus play a crucial role in enhancing the visual complexity of the fractal by introducing smaller, secondary branches that break up the regularity of the main branches, making the structure more detailed and lifelike.</pre><p>9. Color Definition Based on Depth</p><p>% Define color based on depth, simulating a gradient effect
% as recursion deepens
boja = [1 - (prstiter / r), 1 - 0.5 * (prstiter / r), 0];
Line 46: Defines the color boja as a gradient that shifts from yellow to dark orange based on recursion depth. This gradient effect enhances the visual depth of the pattern.
This code sets up a color gradient for each branch segment based on its recursion depth. This approach not only adds aesthetic appeal but also visually separates different levels of recursion, making it easier to perceive depth within the fractal. The variable boja is an RGB color array, where each element represents the intensity of red, green, and blue respectively, on a scale from 0 (no intensity) to 1(full intensity).
The first element, 1 - (prstiter / r), controls the red component. The second element, 1 - 0.5 * (prstiter / r), controls the green component. The third element is set to 0, meaning there is no blue in the color, resulting in a gradient that shifts from yellow (where both red and green are high) to darker orange and then brownish tones as recursion deepens. The color gradually shifts from a bright yellowish tone at shallow recursion levels to a darker, warmer orange as recursion depth increases. This is achieved by gradually decreasing the red and green components of the color as prstiter (current recursion depth) approaches r (maximum recursion depth). At the top levels of recursion (where prstiter is closer to r), the color becomes darker and more subdued, giving the branches a gradient that makes the structure look natural and complex. This effect is reminiscent of how colors in nature tend to fade or darken with distance or depth, such as in underwater scenes where light penetration decreases with depth.
The gradient serves as a visual cue that helps distinguish between different recursion levels. Since each level is progressively darker, viewers can intuitively sense the depth of each branch, which adds to the three-dimensional effect of the fractal. The use of warm colors (yellow to orange) for each branch segment helps the fractal pattern stand out vividly against the cool blue background set in the seaweed function. This color contrast enhances the underwater, organic look of the structure, making it appear as though the "seaweed" is reaching out toward a light source above. This coloring strategy also contributes to the fractal’s aesthetic complexity. By associating color depth with recursion depth, the fractal appears to have layers, creating a visually satisfying and realistic effect.</p><p>10. Plotting Branch Segments</p><p>% Plot main branches from the starting point (tck) to the calculated
% endpoints with color and transparency
p1 = plot([tck(1), b1], [tck(2), a1], 'LineWidth', sir, 'Color', boja);
hold on
s2 = plot([tck(1), a2], [tck(2), c2], 'LineWidth', sir, 'Color', boja);
s3 = plot([tck(1), c3], [tck(2), b3], 'LineWidth', sir, 'Color', boja);
s4 = plot([tck(1), e4], [tck(2), d4], 'LineWidth', sir, 'Color', boja);</p><p>% Plot secondary branches connecting midpoints for added detail
s5 = plot([a2, ugb3], [c2, uga2], 'LineWidth', sir, 'Color', boja);
s6 = plot([c3, ugda1], [b3, ugc2], 'LineWidth', sir, 'Color', boja);
Lines 48-56: Plots the main branches and secondary branches for added detail. Each plot command connects points with a specified thickness and color, creating the branching effect.
Here presented code, plots the main branches and additional “leaf” segments, giving form to the fractal pattern. Each plot command specifies a line segment by connecting two points, with attributes like line width (sir) and color (boja) enhancing the realism and aesthetic detail. Lines from p1to s4 represent a branch extending outward from the current point tck to its calculated endpoint. The branch segments p1, s2, s3, and s4 form the primary structure of the fractal by branching off at angles ug1, ug2, ug3, and ug4 respectively, calculated in earlier presented and explained steps. The plot command takes a pair of [x, y] coordinates that define the line’s start and end points. For instance, p1 = plot([tck(1), b1], [tck(2), a1], 'LineWidth', sir, 'Color', boja); draws a line from tck(the current position) to (b1, a1), one of the endpoints.
The arguments 'LineWidth', sir and 'Color', boja ensure that each line segment has a thickness and color appropriate to its recursion level, making higher-level branches thicker and more prominent while creating a natural gradient. The command hold on is crucial here, it allows MATLAB to draw multiple line segments within the same figure window without erasing the previous segments. This is necessary for the recursive nature of the fractal, as each call to crtaadds branches to the existing structure, layering them to form a complex, interconnected pattern. Lines s5 and s6 represent additional “leaf”segments, plotted between midpoints calculated in Section 8. These smaller branches diverge from the main branches, adding further intricacy and detail to the fractal. By connecting midpoints (such as a2 to ugb3 and c3 to ugda1), the code generates extra “leafy” offshoots that break up the regularity of the main branches.
These segments make the fractal look more organic, akin to the smaller branches and leaves one might see on real plants or seaweed. Similar to the main branches, the secondary branches use sir and boja for line width and color, ensuring consistent visual depth and blending them seamlessly into the overall pattern. This layering allows the fractal to resemble natural structures like foliage or underwater vegetation. The combination of primary and secondary branches contributes to both symmetry and asymmetry in the fractal. While the primary branches provide a balanced, four-way split, the secondary branches introduce slight irregularities, which lend an organic feel to the pattern. Finally, by plotting each segment separately, the code achieves a highly customizable structure. Line thickness, color, and endpoint coordinates can be easily adjusted for each recursion level, allowing flexibility in the appearance and feel of the fractal.</p><p>11. Setting Transparency and Recursion</p><p>% Set transparency for each plot segment
s1.Color(4) = 0.95;
s2.Color(4) = 0.95;
s3.Color(4) = 0.95;
s4.Color(4) = 0.95;
s5.Color(4) = 0.95;
s6.Color(4) = 0.95;</p><p>% Continue recursive drawing if there are levels left ( prstiter > 0)
if prstiter - 1 > 0
% Recursive calls for each of the main branches with
% updated angles and decreased recursion depth
crta([b1, a1], ug1, prstiter - 1, r);
crta([ugb3, uga2], uga1, prstiter - 1, r);
crta([ugda1, ugc2], ugb2, prstiter - 1, r);
crta([e4, d4], ug4, prstiter - 1, r);
end
end
end
Lines 58-63: Sets the transparency of each branch segment to 0.95, creating a slightly translucent effect.
Lines 65-71: Checks if recursion should continue (i.e., if prstiter > 0). If so, the crtafunction recursively calls itself with updated angles and positions, generating the next level of branching until prstiterreaches the value of 0.
This code applies transparency to each branch segment to enhance the visual layering effect and initiates further recursion for drawing deeper levels of the fractal. Lines s1.Color(4) = 0.95; through s6.Color(4) = 0.95; apply transparency to each of the plot segments, allowing branches to be slightly see-through. In MATLAB, the fourth element of the Color property, Color(4), represents the alpha (transparency) value. That is, setting it to 0.95 makes each branch segment 95% opaque, meaning it is just translucent enough to create a layered effect where overlapping branches blend slightly. This subtle transparency creates depth, giving the impression that some branches are behind others, which enhances the natural, three-dimensional appearance of the fractal structure. The transparency effect also softens the overall image, making the fractal appear less rigid and more fluid in water.
Line: if prstiter - 1 > 0, checks if further recursion should occur by verifying that prstiter (the current recursion depth) is greater than 1. If prstiter is greater than 1, the function proceeds to recursively call crta, reducing prstiter by 1 with each call. This gradual reduction in prstiter ensures that recursion continues until the maximum depth, defined by r, is reached. As the recursion depth decreases with each call, the branch segments become progressively shorter and thinner, creating a tapered effect that adds to the realistic, fractal-like branching.
Recursive Calls of the function crta, calls itself four times, once for each main branch direction (ug1, ug2, ug3, ug4), using updated coordinates and angles:
crta([b1, a1], ug1, prstiter - 1, r); initiates a recursive call for the branch at angle ug1.
crta([ugb3, uga2], uga1, prstiter - 1, r); starts recursion from the midpoint branch at angle uga1.
crta([ugda1, ugc2], ugb2, prstiter - 1, r); continues recursion from the midpoint branch at angle ugb2.
crta([e4, d4], ug4, prstiter - 1, r); initiates recursion from the branch at angle ug4.
Each recursive call passes a new starting point (calculated in previous steps) and an adjusted angle. These recursive calls add the next level of branching, gradually building out the entire fractal structure. The recursive calls are fundamental to constructing the fractal pattern. By creating multiple levels of branching, each progressively smaller and more complex, the fractal develops a rich, layered structure that mimics natural growth patterns. The recursive structure also allows for variations in each level, as each branch is influenced by slightly different angles and positions, resulting in an organic, non-uniform look. This natural irregularity is key to creating a visually appealing fractal. Additionally, since each recursive call has transparency applied to its branches, the resulting fractal has a soft, blended appearance. Overlapping branches appear to merge gently, creating a cohesive, three-dimensional visual effect.</p><p>End of Code
end
This line closes the entire drawframe function, completing the recursive fractal drawing of the seaweed structure.
Sometimes, neglecting to include the necessary closure for a function can lead to unexpected surprises in the code. Always be vigilant about ensuring that functions, loops, and other structures are properly closed.</p><p>Summary: This whole code uses recursion and geometry to create natural-looking, fractal-inspired patterns that mimic the movement and appearance of seaweed, achieving complexity and organic flow through simple recursive structure and dynamic angle variations.</p>Teodohttps://jp.mathworks.com/matlabcentral/profile/authors/7095160tag:jp.mathworks.com,2005:Topic/8764342024-10-21T22:12:44Z2024-11-04T22:59:59ZSchwarzschild Radius: The Edge of Darkness<pre> Inspired by the suggestion of Mr. Chen Lin (MathWorks), I am writing this post with a humble and friendly intent to share some fascinating insights and knowledge about the Schwarzschild radius. My entry, which is related to this post, is named: 'Into the Abyss - Schwarzschild Radius (a time lapse)'.</pre><pre> The Schwarzschild radius (or gravitational radius) defines the radius of the event horizon of a black hole, which is the boundary beyond which nothing, not even light, can escape the gravitational pull of the black hole. This concept comes from the Schwarzschild solution to Einstein’s field equations in general relativity. Black holes are regions of spacetime where gravitational collapse has caused matter to be concentrated within such a small volume that the escape velocity exceeds the speed of light.
This is a rudimentary scientific post, as the matter of Schwarzschild radius - it's true meaning and function, is a much, much, much-more complex "thing" (not known to us entierly, by the third degre of epistemological explanation(s)).
And, very important is to mention: I am NOT an expert - by any means, on this topic, just a very curious guy, in almost anything, that has to do with science.</pre><p>Schwarzschild Radius (Gravitational Radius)
The Schwarzschild radius (Rₛ) is the critical radius at which an object of mass must be compressed to form a black hole, specifically, a non-rotating, uncharged black hole, known as a Schwarzschild black hole. The Schwarzschild radius is given by the formula: .
Where: .
Key Characteristics are, that for any mass, if that mass is compressed within a sphere with radius equal to , the gravitational field is so strong that not even light can escape, thus forming a black hole. The Schwarzschild radius is proportional to the mass. Larger masses have larger Schwarzschild radii.
Example:
For the Sun : .
So, if the Sun were compressed into a sphere with a radius of ~3 km, it would become a black hole!
Stellar-mass Black Holes form from the collapse of massive stars (roughly ). Their Schwarzschild radius ranges from a few kilometers to tens of kilometers.
Supermassive Black Holes found at the centers of galaxies, such as Sagittarius A in the Milky Way (), their Schwarzschild radii span from a few million to billions of kilometers!
Primordial or Micro Black Holes, are the hypothetical small black holes with masses much smaller than stellar masses, where the Schwarzschild radius could be extremely tiny.
A black hole, in general, is a solution to Einstein’s general theory of relativity where spacetime is curved to such an extent that nothing within a certain region, called the event horizon, can escape.</p><p>Types of Black Holes:
1. Schwarzschild (Non-rotating, Uncharged):
- This is the simplest type of black hole, described by the Schwarzschild solution.
- Its key feature is the singularity at the center, where the curvature of spacetime becomes infinite.
- No charge, no angular momentum (spin), and spherical symmetry.
2. Kerr (Rotating):
- Describes rotating black holes.
- Involves an additional parameter called angular momentum.
- Has an event horizon and an inner boundary, known as the ergosphere, where spacetime is dragged around by the black hole's rotation.
3. Reissner–Nordström (Charged, Non-rotating):
- A black hole with electric charge.
- A charged black hole has two event horizons (inner and outer) and a central singularity.
4. Kerr–Newman (Rotating and Charged):
- The most general solution, describing a black hole that has both charge and angular momentum.</p><p>Relationship Between Schwarzschild Radius and Black Holes
Formation of Black Holes: When a massive star exhausts its nuclear fuel, gravitational collapse can compress the core beyond the Schwarzschild radius, creating a black hole.
Event Horizon: The Schwarzschild radius marks the event horizon for a non-rotating black hole. This is the boundary beyond which no information or matter can escape the black hole.
Curvature of Spacetime: At distances closer than the Schwarzschild radius, spacetime curvature becomes so extreme that all paths, even those of light, are bent towards the black hole’s singularity.
BTW, the term singularity, scientificaly 😊, means that: we do not have a clue what is really happening right there...</p><p>Detailed Properties of Black Holes:
a. Singularity:
At the center of a black hole, within the Schwarzschild radius, lies the singularity, a point (or ring in the case of rotating black holes) where gravitational forces compress matter to infinite density and spacetime curvature becomes infinite. General relativity breaks down at the singularity, and a quantum theory of gravity is required for a complete understanding.
b. Event Horizon:
The event horizon is not a physical surface but a boundary where the escape velocity equals the speed of light. For an outside observer, objects falling into a black hole appear to slow down and fade away near the event horizon due to gravitational time dilation, a prediction of general relativity. From the perspective of the infalling object, however, it crosses the event horizon in finite time without noticing anything special at the moment of crossing.
c. Hawking Radiation: (In the post, I told that there is no radiation - to make it simple, although, there is a relatively newly-found (theoretically) radiation. Truth to be said, some physicists are still chalenging this notion, in some of it's parts...)
Quantum mechanical effects near the event horizon predict that black holes can emit radiation (Hawking radiation), a process through which black holes can lose mass and, over very long timescales, potentially evaporate completely. This process has a temperature inversely proportional to the black hole's mass, making large black holes emit extremely weak radiation. (Very trivialy speaking: the concept supposes that an anti-particle is drawn from the vakum and is anihilated with the black's hole matter (particle), and in the process, the black hole looses mass gradually and proportionally to the released energy - very slowly(!)).</p><p>This radiation is significant only for small black holes.</p><p>Gravitational Time Dilation (here, as well, things become 'super-weird'...)
Near the Schwarzschild radius, the intense gravitational field leads to time dilation. For an external observer far from the black hole, time appears to slow down for an object moving toward the event horizon. As it approaches the Schwarzschild radius, time dilation becomes so extreme that the object appears frozen in time at the horizon.
The time dilation factor is given by:
Eg. Approaching the Schwarzschild radius and theoretically remaining just outside of it for a few hours would correspond to the passage of approximately several decades on Earth due to relativistic time dilation.
Using relativistic equations, it's estimated that near the event horizon 2 hours (120 minutes) near the black hole Sagittarius A* (as already mentioned ~ 4 million ) - in the center of our galaxy Milky Way, could correspond to 83 years passing on Earth! However, this varies based on the precise distance from the event horizon (give or take, a decade 😬).</p><p>Information Paradox (definte answer on this question, 'hold's the keys of the universe' 😊, maybe...)
The black hole information paradox arises from the seeming contradiction between general relativity and quantum mechanics.
According to quantum mechanics, information cannot be destroyed, yet anything falling into a black hole seems to be lost beyond the event horizon. Hawking radiation, which allows a black hole to evaporate, does not appear to carry information about the matter that fell into the black hole, leading to ongoing debates and research into how information is preserved in the context of black holes, or not...!
Schwarzschild Radius is the key parameter defining the size of the event horizon of a non-rotating black hole. Black Holes are regions where the Schwarzschild radius constrains all physical phenomena due to extreme gravitational forces, forming event horizons and singularities. The interaction between general relativity and quantum mechanics in the context of black holes (e.g., Hawking radiation and the information paradox) remains one of the most intriguing areas in modern theoretical physics.
For detailed and further reading: https://www.sciencedirect.com/topics/physics-and-astronomy/hawking-radiation.</p><p>I hope you will find this post, and information provided, interesting.</p>Teodohttps://jp.mathworks.com/matlabcentral/profile/authors/7095160tag:jp.mathworks.com,2005:Topic/8768722024-11-04T20:11:45Z2024-11-04T21:00:10ZMasking 3D Surfaces and Carving Pumpkins - A Halloween Special!<p>Pumpkins have been a popular, recurring, and ever-evolving theme in MATLAB during the past few years, and particularly during this time of year. Much of this is driven by the epic work of @Eric Ludlam and expanded upon by many others. The list of material is too extensive to go through everything individually, but I'm listing some of my favourite resources below and I highly recommend these to everyone as they're a lot of fun to play with:
Gourds to Graphics: The MATLAB Pumpkin
Pumpkin Designer
Pumpkins are also particularly prominent during the yearly Mini Hack Contests. This year, I have jumped onto the bandwagon myself with my Floating Pumpkins entry:</p><p>In this post, I would like to introduce the concept of masking 3D surfaces in a festive and fun way, by showcasing how to apply it for carving faces on pumpkins step by step.
Let's start by drawing the pumpkin's body. The following was adapted from Eric's code:
n = 600; % Number of faces</p><p>% Shape pumpkin's rind (skin)
[X,Y,Z] = sphere(n);</p><p>% Shape pumpkin's ribs (ridges)
R = (1-(1-mod(0:20/n:20,2)).^2/12);
X = X.*R; Y = Y.*R; Z = Z.*R;
Z = (.8+(0-linspace(1,-1,n+1)'.^4)*.3).*Z;</p><p>function plotPumpkin(X,Y,Z)
figure
surf(X,Y,Z,'FaceColor',[1 .4 .1],'EdgeColor','none');
hold on
box on
axis([-1 1 -1 1 -1 1],'square')
xlabel('x'); xticks(-1:0.5:1)
ylabel('y'); yticks(-1:0.5:1)
zlabel('z'); zticks(-1:0.5:1)
material([.45,.7,.25])
camlight('headlight')
camlight('headlight')
lighting gouraud
end</p><p>plotPumpkin(X,Y,Z)
The next step is drawing the face for the mask. This can be done in 2D and can consist of any number of lines that form polygonal closed shapes and are appropriately scaled relative to the coordinates of the pumpkin. A quick example:
% Mouth
xm = [-.5:.1:.5 flip(-.5:.1:.5)];
ym = [.15 -.3 -.25 -.5 -.4 -.6 flip([.15 -.3 -.25 -.5 -.4]) .15 -.05 0 -.25 -.15 -.3 flip([.15 -.05 0 -.25 -.15])];</p><p>% Right eye
xr = [-.35 -.05 -.35];
yr = [.1 0 .5];</p><p>% Left eye
xl = abs(xr);
yl = yr;</p><p>figure('Color','w')
set(gcf,'Position',get(gcf,'Position')/2)
axes('Visible','off','NextPlot','Add')
axis tight square
fill(xm,ym,'k')
fill(xr,yr,'k')
fill(xl,yl,'k')
We then need to apply the 2D mask to the 3D surface. To do that, we project it onto the intersections of the surface with the XY plane. However, as we need the face to appear on the side of the pumpkin, we first need to rotate the pumpkin so that the front side is facing upwards. Essentially, we need to rotate the pumpkin around the x-axis by -π/2 rad.
Let's do this from first principles to better understand the process:
theta = [-pi/2,0,0];
[X,Y,Z] = xyzRotate(X,Y,Z,theta);</p><p>function [X,Y,Z] = xyzRotate(X,Y,Z,theta)
% Rotation matrices
Rx = [1 0 0;0 cos(theta(1)) -sin(theta(1));0 sin(theta(1)) cos(theta(1))];
Ry = [cos(theta(2)) 0 sin(theta(2));0 1 0;-sin(theta(2)) 0 cos(theta(2))];
Rz = [cos(theta(3)) -sin(theta(3)) 0;sin(theta(3)) cos(theta(3)) 0;0 0 1];
for i=1:size(X,1)
for j=1:size(X,2)
r=Rx*Ry*Rz*[X(i,j);Y(i,j);Z(i,j)];
X(i,j)=r(1);
Y(i,j)=r(2);
Z(i,j)=r(3);
end
end
end
More information about these transformations can be found here:
rotx - Rotation matrix for rotations around x-axis
Matrix Rotations and Transformations
When plotting we get:
plotPumpkin(X,Y,Z)
Note that as we have only rotated this around the x-axis, Ry and Rz are equal to eye(3).
We can now apply the mask as discussed. We do this by using one of my favourite functions inpolygon. This gives us the corresponding indices of all the data points located inside our polygonal regions. At this stage, it's important to keep the following in mind:
The number of faces (n) controls the discretization of the pumpkin. The larger it is, the smoother the mask will be, but at the same time the computational cost will also increase. If you are using this for the contest which has a timeout limit of 235 seconds, you might need to adjust it accordingly.
You will also need to restrict the Z-coordinates appropriately (Z>=0) so that the mask is only applied on the front side of the pumpkin.
If you are animating the face mask (more information about this below), and you need the eyes and mouth to fully close at any point, avoid using the second argument of the inpolygon function that gives you the points located on the edge of the regions.
The masking function is given below:
function [X,Y,Z] = Mask(X,Y,Z,xm,ym,xr,yr,xl,yl)
mask = ones(size(Z));
mask((inpolygon(X,Y,xm,ym)|inpolygon(X,Y,xr,yr)|inpolygon(X,Y,xl,yl))&Z>=0) = NaN;
Z = Z.*mask;
end
Applying the mask gives us:
[X,Y,Z]=Mask(X,Y,Z,xm,ym,xr,yr,xl,yl);
plotPumpkin(X,Y,Z)
arrayfun(@(x)light('style','local','position',[0 0 0],'color','y'),1:2)
We can see that MATLAB was thoughtful enough to automatically remove the pulp from inside the pumpkin, proving its convenience time and time again.
We can then rotate the pumpkin back and add the stem to get the final result:
theta = [pi/2,0,0];
[X,Y,Z] = xyzRotate(X,Y,Z,theta);</p><p>% Stem
s = [1.5 1 repelem(.7, 6)] .* [repmat([.1 .06],1,round(n/20)) .1]';
[t,p] = meshgrid(0:pi/15:pi/2,linspace(0,pi,round(n/10)+1));</p><p>Xs = repmat(-(.4-cos(p).*s).*cos(t)+.4,2,1);
Ys = [-sin(p).*s;sin(p).*s];
Zs = repmat((.5-cos(p).*s).*sin(t)+.55,2,1);</p><p>plotPumpkin(X,Y,Z)
arrayfun(@(x)light('style','local','position',[0 0 0],'color','y'),1:2)
surf(Xs,Ys,Zs,'FaceColor','#008000','EdgeColor','none');
And that's it. You can now add some change to the mask's coordinates between frames and play around with the lighting to get results such as these (more information on how to do this on my Teaser entry):</p><p>I hope you have found this tutorial useful, and I'm looking forward to seeing many more creative entries during the final week of the contest.</p>Vasilis Belloshttps://jp.mathworks.com/matlabcentral/profile/authors/13754969tag:jp.mathworks.com,2005:Topic/8768682024-11-04T18:33:41Z2024-11-04T19:44:42ZVote on MATLAB Short Movies and win MATLAB T-shirts Before Nov. 10th!<p>What incredible short movies can be crafted with no more than 2000 characters of MATLAB code? Discover the creativity in our GALLERY from the MATLAB Shorts Mini Hack contest.
Vote on your favorite short movies by Nov.10th. We are giving out MATLAB T-shirts to 10 lucky voters!</p><p>Tips: the more you vote, the higher your chance to win.</p>Chen Linhttps://jp.mathworks.com/matlabcentral/profile/authors/6682740tag:jp.mathworks.com,2005:Topic/8762412024-10-15T22:41:20Z2024-11-04T19:32:33ZMini Hack Shorts Week 1 Winners Announced! Plus Tips for Week 2<p>There are so many incredible entries created in week 1. Now, it’s time to announce the weekly winners in various categories!</p><p>Nature & Space:
Jenny Bosten / Then and now
Oliver Jaros / Winter
KARUPPASAMYPANDIYAN M / Nightfall Harmony!
Tim / Moon elevator</p><p>Seamless Loop:
Edgar Guevara / EKG pulse
Tomoaki Takagi / Octagram</p><p>Abstract:
Malik / Fragility
Andrew / Rotor Acoustic Interference (Intensity)</p><p>Remix of previous Mini Hack entries:
Vasilis Bellos / Isle of Thunderstorms
Jr / 1/3 - Litany Against Fear</p><p>Early Discovery
Hiroshi Iwamura / Manta Race</p><p>Holiday:
SHRABASTI / Halloween</p><p>Congratulations to all winners! Each of you won your choice of a T-shirt, a hat, or a coffee mug. We will contact you after the contest ends.</p><p>In week 2, we’d love to see and award more entries in the ‘Seamless Loop’ category. We can't wait to see your creativity shine!</p><p>Tips for Week 2:
1.Use AI for assistance
The code from the Mini Hack entries can be challenging, even for experienced MATLAB users. Utilize AI tools for MATLAB to help you understand the code and modify the code. Here is an example of a remix assisted by AI. @Hans Scharler used MATLAB GPT to get an explanation of the code and then prompted it to ‘change the background to a starry night with the moon.’
2. Share your thoughts
Share your tips & tricks, experience of using AI, or learnings with the community. Post your knowledge in the Discussions' general channel (be sure to add the tag 'contest2024') to earn opportunities to win the coveted MATLAB Shorts.
3. Ensure Thumbnails Are Displayed:
You might have noticed that some entries on the leaderboard lack a thumbnail image. To fix this, ensure you include ‘drawframe(1)’ in your code.</p>Chen Linhttps://jp.mathworks.com/matlabcentral/profile/authors/6682740tag:jp.mathworks.com,2005:Topic/8767792024-11-01T19:39:11Z2024-11-04T14:11:33ZSeveral fancy functions.<p>Hi everyone, I wrote several fancy functions that may help your coding experience, since they are in very early developing stage, I will be thankful if anyone could try them and give some feedbacks. Currently I have following:
fstr: a Python f-string like expression
printf: an easy to use fprintf function, accepts multiple arguments with seperator, end string control.
I will bring more functions or packages like logger when I am available.
The code is open sourced at GitHub with simple examples: https://github.com/bentrainer/MMGA</p>Zhihao Huhttps://jp.mathworks.com/matlabcentral/profile/authors/18913577tag:jp.mathworks.com,2005:Topic/8762792024-10-17T00:28:34Z2024-11-04T13:39:13ZDynamic Data Visualization in MATLAB<pre> Here presented MATLAB code is designed to create a seamless loop animation that visualizes an isosurface derived from random data.
This entry, titled "The Scrambled Predator's Cube", builds upon my previous work and has been adapted to include dynamic elements.</pre><pre> In this explanation, I will break down the relatively short code, making it accessible whether you are a beginner in MATLAB or an experienced user. Let's go through the MATLAB code step by step to understand each line in detail.</pre><p>Code Breakdown</p><p>d = rand(8,8,8);</p><pre> Random Data Generation: This line creates a three-dimensional array d with dimensions 8×8×8 filled with random values. The rand function generates values uniformly distributed in the interval (0,1). This array serves as the input data for generating the isosurface.</pre><p>iv = .5 + (f / 10000);</p><pre> Isovalue Calculation: Here, the isovalue iv is computed based on the frame number f. The expression f / 10000 causes iv to increase very slowly as f increments. Starting from 0.50, this means that for every increment of f, iv changes slightly (specifically, by 0.0001). This gradual increase creates a smooth transition effect in the isosurface over time, making it look dynamic as the animation progresses.</pre><p>h = patch(isosurface(d, iv), 'FaceColor', 'blue', 'EdgeColor', 'none');</p><pre> Isosurface Creation: The isosurface function extracts a 3D surface from the data array d at the specified isovalue iv. The result is a patch object h that represents the isosurface in the 3D plot. The 'FaceColor', 'blue' argument sets the face color of the surface to blue, while 'EdgeColor', 'none' specifies that no edges should be drawn, giving the surface a solid appearance.</pre><p>isonormals(d, h);</p><pre> Surface Normals Calculation: This function calculates the normals at each vertex of the isosurface h, based on the data in d. Normals are vectors perpendicular to the surface at each point and are crucial for proper lighting calculations. By using isonormals, the appearance of depth and texture is enhanced, allowing the lighting to interact more realistically with the surface.</pre><p>patch(isocaps(d, iv), 'FaceColor', 'interp', 'EdgeColor', 'none');</p><pre> Isocaps Visualization: The isocaps function creates flat surfaces (caps) at the boundaries of the isosurface where the data values meet the isovalue iv. The resulting caps are then rendered as patches with 'FaceColor', 'interp', meaning the colors of the caps are interpolated based on the data values. The caps provide a more complete visual representation of the isosurface, improving its overall appearance.</pre><p>colormap hsv;</p><pre> Color Map Setup: This line sets the colormap of the current figure to HSV (Hue, Saturation, Value). The HSV colormap allows for a wide range of colors, which can enhance the visual appeal of the rendering by mapping different values in the data to different colors.</pre><p>daspect([1, 1, 1]);</p><pre> Aspect Ratio Setting: The daspect function sets the data aspect ratio of the plot to be equal in all three dimensions. This means that one unit in the x-direction is the same length as one unit in the y-direction and z-direction, ensuring that the visual representation of the 3D data is not distorted.</pre><p>axis tight;</p><pre> Tight Axis Setting: This command adjusts the limits of the axes so that they fit tightly around the data, removing any excess white space. It helps to focus the viewer's attention on the isosurface and related visual elements.</pre><p>view(3);</p><pre> 3D View Configuration: The view(3) command sets the current view to a 3D perspective, allowing the viewer to see the structure of the isosurface from an angle that reveals its three-dimensional nature.</pre><p>camlight right;
camlight left;</p><pre> Lighting Effects: These commands add two light sources to the scene, positioned to the right and left of the view. The additional lighting enhances the shading and depth perception of the isosurface, making it appear more three-dimensional and visually appealing.</pre><p>axis off;</p><pre> Hide Axes: This command turns off the display of the axes in the plot. Removing the axes provides a cleaner visual representation, allowing the viewer to focus solely on the isosurface and its lighting effects without distraction from the grid lines or axis labels.</pre><p>lighting phong;</p><pre> Lighting Model: This line sets the lighting model to Phong. The Phong model is widely used in computer graphics as it provides smooth shading and realistic reflections. It calculates how light interacts with surfaces, enhancing the overall appearance by creating a more natural look.</pre><pre> This code creates a visually dynamic and appealing representation of an isosurface derived from random data. The gradual change in the isovalue allows for smooth transitions, while the combination of lighting, colors, and shading contributes to a rich 3D visualization. Each component plays a vital role in rendering the final output, showcasing advanced techniques in data visualization using MATLAB.</pre>Teodohttps://jp.mathworks.com/matlabcentral/profile/authors/7095160tag:jp.mathworks.com,2005:Topic/8513062022-03-14T11:28:43Z2024-11-04T00:57:42ZMathworks: it's time for a dark theme.<p></p>Antonello Zitohttps://jp.mathworks.com/matlabcentral/profile/authors/17193431tag:jp.mathworks.com,2005:Topic/8740492024-08-16T11:25:15Z2024-11-03T12:49:50ZDrone for Matlab<p>Hi everyone, I am from India ..Suggest some drone for deploying code from Matlab.</p>Salam Surjithttps://jp.mathworks.com/matlabcentral/profile/authors/11868646tag:jp.mathworks.com,2005:Topic/8767212024-10-31T10:05:42Z2024-11-02T18:45:42ZPrime Numbers ... with a Regular Expression!<p>I know we have all been in that all-too-common situation of needing to inefficiently identify prime numbers using only a regular expression... and now Matt Parker from Standup Maths helpfully released a YouTube video entitled "How on Earth does ^.?$|^(..+?)\1+$ produce primes?" in which he explains a simple regular expression (aka Halloween incantation) which matches composite numbers:
https://www.youtube.com/watch?v=5vbk0TwkokM
Here is my first attempt using MATLAB and Matt Parker's example values:
fnh = @(n) isempty(regexp(repelem('*',n),'^.?$|^(..+?)\1+$','emptymatch'));
fnh(13)
fnh(15)
fnh(101)
fnh(1000)
Feel free to try/modify the incantation yourself. Happy Halloween!</p>Stephen23https://jp.mathworks.com/matlabcentral/profile/authors/3102170tag:jp.mathworks.com,2005:Topic/8767262024-10-31T11:35:46Z2024-11-02T06:10:53ZHow long (T) have you been using Matlab for ?Nicolas Douillethttps://jp.mathworks.com/matlabcentral/profile/authors/8668631tag:jp.mathworks.com,2005:Topic/8767832024-11-01T22:57:48Z2024-11-01T22:57:48ZExperience Insight and Innovation with Keynote Speaker, María Elena Gavilán Alfonso!<p>Mark your calendar for November 13–14 and get ready for two days of learning, inspiration, and connections!
We are thrilled to announce that MathWork’s incredible María Elena Gavilán Alfonso was selected as a keynote speaker at this year’s MATLAB Expo.
Her session, "From Embedded to Empowered: The Rise of Software-Defined Products," promises to be a game-changer! With her expertise and insights, María is set to inspire and elevate our understanding of the evolving world of software-defined products.
Watch a sneak peek here and get a taste of what's to come!
Interested in attending? Sign up at matlabexpo.com/online</p>Chen Linhttps://jp.mathworks.com/matlabcentral/profile/authors/6682740