Plot by equation.

I have an equation for ploting;

x=1 to 10 nanometers ;

y=0.5 to 2 nanometers;

and k=1 to 10;(not nanometers it is a multiplication)

the equation is:

f=8.854187817.*(x.*x.*k.^2)/(y.*y);

and i need a plot for all k values from 1 to 10;

plot(f,k); ant this didn t work;

Answer 1

[Walter Roberson]

x = linspace(1,10,15);
y = linspace(0.5,2,15);
k = linspace(1,10,15);
[X,Y,K] = meshgrid(x, y, k);
f = 8.854187817.*(X.*X.*K.^2)./(Y.*Y);

However, this is essentially 4D -- three input coordinates and one result. Even if you divide it up by k value, the result would be 3D for each k value, which would make it a bit difficult to plot everything at the same time. What kind of plots were you hoping for?

pointsize = 36;
scatter3(X(:),Y(:),K(:),pointsize,f(:))

or

slice(X,Y,K,f,[],[],k)

[Image Analyst]

"three input coordinates and one result" is what I call 3D. Such data can be stored in a 3-D array. For example a volumetric image, like CT or MRI, where you have (x,y,z) coordinates and a value (like temperature, density, signal, or whatever) for each location. It can be visualized with 3D volumetric visualization programs like Avizo.

And ndims(f) reports 3.

[Walter Roberson]

You can position on the three spatial dimensions, but for each combination of spatial dimensions you have a result that has to be plotted somehow. You cannot plot that as a 4th spatial dimension the way you can plot the height of a surface defined with two free parameters. You have to find another way to plot the 4th piece of information (the value of f). One way to do that is color; another way is to plot through time.

Mathematically, 3 input values plus one result is referred to as 4D, because you can itemize each output as a 4-tuple,

(x, y, k, f)

and mathematically "functions" are fundamentally tuples (formula are short-hand for listing all of the tuples.)

[Stephen23]

ionescu andrei's "Answer" moved here:

but how i make k natural with values between 1 to 10?

Answer 2

[ionescu andrei]

and how can i se value of F in (f) the plot?