Plotting iteratively defined function in MATLAB - 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