How to quantify density of lines in a plot?

Kind all,

I am using a Monte Carlo approach to explore the paramter space of a model. The outputs are different lines that corresponds to the variation of my model's endpoint due to the parameters' variation. Is there a way to realize a contour plot of the density of such realizations?

For the sake of exemplifcation let's assume that my model is the simple function:

func=@(x,m,c)(m*x.^2+c)

x are my data (a fixed vector of inputs to the model), while m and c are parameters that vary within a range.

Now let's assume that:

x=[1:10];
max_m=10;
min_m=0.5;
max_c=max_m;
min_c=min_m;
iterations=1000;

And let our Monte Carlo approach run:

    % initialize colors for the plot
     cc=hsv(iterations);
    % let our model run and plot results:
     for k=1:iterations;
        m=(max_m-min_m).*rand+min_m;
        c=(max_c-min_c).*rand+min_c;
        out=func(x,m,c);
        hold on
        plot(out,'color',cc(k,:));
     end

This would result in the following plot:

Is there a way to get an information on how dense/overlapped the lines in the plot in order to either generate a contour or an imagesc plot of the parameter space?

Thanks, all!