create a fractal in matlab in matlab

main.m
% Define the size of the image
width = 800;
height = 800;

% Define the region of interest in the complex plane
xlim = [-2.5, 1];
ylim = [-1.5, 1.5];

% Generate the grid of complex numbers spanning the region of interest
[X, Y] = meshgrid(linspace(xlim(1), xlim(2), width), linspace(ylim(1), ylim(2), height));
C = X + 1i * Y;

% Create an empty matrix to store the fractal pattern
fractal = zeros(size(C));

% Set the maximum number of iterations for each complex number
maxIterations = 100;

% Perform the iteration for each complex number
Z = zeros(size(C));

for n = 1:maxIterations
    Z = Z.^2 + C;
    mask = abs(Z) < 100;
    fractal(mask) = n;
end

% Plot the fractal pattern
imshow(fractal, 'Colormap', jet(maxIterations));
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