Plotting iteratively defined function in MATLAB

Question

I'm not a MATLAB professional and so, I need some help at producing a 3D plot of the iteratively defined function f : R^2-0 -> R defined below (in pseudocode) for x,y values in [-1,1] and

For each I = 1,2,3 and A = (0.5,0.5)

function  f(v in R^2-0)
{
    a=b=0;     (a,b in R)        
    for (i=0; i<I; i=i+1)
    {
        v = |v| / ||v||^2 - A;
        a = a + | ||v||-b |;
        b = ||v||;
    }
    return a;
}

(|v| denotes component-wise vector absolute value)

(If you want you can look at the fractal that is generated by the function at my question on math-exchange here:

https://math.stackexchange.com/questions/1457733/a-question-about-a-fractal-like-iteratively-defined-function )

MATLAB code to do that will be appreciated.

Much Thanks.

Answer 1

Save this your main program:

clear
clc
close all

% I = 1;
% A = [ 0.5 0.5 ];

I = 10;
A = [ 0.5 0.5 0.5 ];

xmin = -1;
xmax = 1;

ymin = -1;
ymax = 1;

nx = 101;
ny = 101;

dx = (xmax - xmin) / (nx - 1);
dy = (ymax - ymin) / (ny - 1);

x = xmin: dx: xmax;
y = ymin: dy: ymax;

for ix = 1: nx
    for iy = 1: ny
        if (length(A) == 2)
            z(iy, ix) = f([x(ix) y(iy)], A, I);
        elseif (length(A) == 3)
            z(iy, ix) = f([x(ix) y(iy) 0], A, I);
        end
    end
end

pcolor(x, y, z)
shading interp

Then save this function in the same directory as the main program as f.m:

function result = f(v, A, I)

a = 0;
b = 0;

for i = 1: I
    v = abs(v) / dot(v, v) - A;
    a = a + abs(norm(v) - b);
    b = norm(v);
end
result = a;

end