a minimal implementation of the mandelbrot set in Matlab

MandelbrotSet.m

grid = 0.01;
iter = 50;

%% mandelbrot set
[Re,Im] = meshgrid(-2:grid:1,-1:grid:1);
z0 = Re + Im*1i; % creates a grid of complex numbers from -2 to 1 on the real axis and from -1 to 1 on the imaginary axis
values = zeros(size(z0));

z = z0;
for n = 1:iter
   z = z.^2 + z0;
   values(abs(z)<=2) = values(abs(z)<=2) + 1; % increment values that are still bounded by 2
end

surf(Re,Im,values,'EdgeColor','none'); view(2);

%% julia set
figure;

c = -0.4 + 0.6i; % defining value for this julia set, can be any other value too

[Re,Im] = meshgrid(-1.5:grid:1.5,-1.5:grid:1.5);
z = Re + Im*1i;
values = zeros(size(z));

for n = 1:iter
   z = z.^2 + c;
   values(abs(z)<=2) = values(abs(z)<=2) + 1; % increment values that are still bounded by 2
end

surf(Re,Im,values,'EdgeColor','none'); view(2);

mandelbrot set

julia set for -0.4 + 0.6i