fractal figure in matlab in matlab

To create a fractal figure in MATLAB, you can use recursive techniques and plotting functions. MATLAB provides a convenient way to generate fractals using recursion.

Here is an example of generating the famous Mandelbrot fractal in MATLAB:

main.m
% Define the size of the figure and the number of iterations
figure_size = 500; % pixels
max_iterations = 1000;

% Create a meshgrid for complex plane coordinates
[X, Y] = meshgrid(linspace(-2, 1, figure_size), linspace(-1.5, 1.5, figure_size));
Z = X + 1i * Y;

% Initialize the fractal image
fractal_image = ones(size(Z));

% Calculate the fractal using the iteration formula: Z_n+1 = Z_n^2 + C
for i = 1:max_iterations
    fractal_image = fractal_image + (abs(Z) <= 2);
    Z = Z.^2 + fractal_image;
end

% Plot the fractal figure
figure;
imagesc(fractal_image);
colormap hot;
axis equal;
axis off;
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This code will generate the Mandelbrot fractal and display it as a figure. You can adjust the figure_size and max_iterations variables to customize the size and level of detail of the fractal.

Note that there are numerous other types of fractals you can create in MATLAB, such as the Julia set or the Sierpinski triangle. The specific technique for generating each fractal may vary, but the fundamental idea is similar: iterate through each point in a complex plane and apply a recursive formula.