[bs] Mandelbrot Set

Referensi : wikipedia

The Mandelbrot set is a mathematical set of points whose boundary is a distinctive and easily recognizable two-dimensional fractalshape. The set is closely related to Julia sets (which include similarly complex shapes), and is named after the mathematician Benoit Mandelbrot, who studied and popularized it.


z = z^2+c

z = z^3+c

z = z^4+c

z = z^5+c

z = z^6+c

z = z^7+c

Matlab code untuk Mandelbrot Set

File 1 : Main Program

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clc

clear all

close all

% Mandelbrot Set

% Edited by Andri Husein

k = 80;       % Number of iterations 100

Xr = [-2 2];  % x-axis range value 

Yr = [-2 2];  % y-axis range value

Mandelbrot_plot(k,Xr,Yr)

xlabel('X-Axis','FontSize',16)

ylabel('Y-Axis','FontSize',16)

title('Mandelbrot Set','FontSize',16)

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File 2 : Function, simpan dengan nama: Mandelbrot_plot

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function Mandelbrot_plot(k,Xr,Yr)

n = 400;

x = linspace(Xr(1,1),Xr(1,2),n);

y = linspace(Yr(1,1),Yr(1,2),n);

[X,Y] = meshgrid(x,y);

W = zeros(length(X),length(Y));

i = sqrt(-1);

for m = 1:size(X,2)

    for j = 1:size(Y,2)

        [w,iter] = Mandelbrot(X(m,j)+Y(m,j)*i,k);

        W(m,j) = W(m,j) + iter;

    end

end

hold on;

%colormap(jet);     %pilihan warna 1

%colormap(winter);  %pilihan warna 2

colormap(hsv);      %pilihan warna 3

%colormap(cool);    %pilihan warna 4

pcolor(W);          %plot 2D

caxis([0 40]);      %rentang nilai warna

shading interp;     %melembutkan grafik

hold off;

%-----------------------------------

function [pri,it] = Mandelbrot(c,m)

k = 0;

z = c;

while k < m

    if abs(z) > 2

        pri = 1;

        it = k;

        return;

    end

    % Ref http://commons.wikimedia.org/wiki/Fractal

    z = z^2 + c;

    %z = z^3+c;

    %z = z^4+c;

    %z = z^5+c;

    %z = z^6+c;

    %z = z^7+c;    

    k = k + 1;

end

pri = 0;

it = k;

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Copyright (c) 2006, Krzysztof Gdawiec

All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

* Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

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