Codes in matlab/octave for generating some popular fractals:

**Mandelbrot**

```
```

`function mandelbrotmain()`

clear variables; clc;

maxit=200;

x=[-2,1];

y=[-1 1];

xpix=601;

ypix=401;

x=linspace(x(1),x(2),xpix);

y=linspace(y(1),y(2),ypix);

[xG, yG]=meshgrid(x,y);

c=mb(maxit,xG,yG);

figure

imagesc(x,y,c);

colormap([1 1 1;0 0 0]);

axis on;

grind on;

endfunction

function count=mb(maxItr,xG,yG)

c=xG+1i*yG;

count=ones(size(c));

z=c;

for n=1:maxItr

z=z.*z+c;

inside=abs(z)<=2;

count=count+inside;

endfor

endfunction

**Sierpinski triangle**

```
```

`clc;`

clear variables;

close windows;

clf

N=500;

x=zeros(1,N);y=x;r=x;

for a=2:N

c=randi([0 2]);

r(a)=c;

switch c

case 0

x(a)=0.5*x(a-1);

y(a)=0.5*y(a-1);

case 1

x(a)=0.5*x(a-1)+.25;

y(a)=0.5*y(a-1)+sqrt(3)/4;

case 2

x(a)=0.5*x(a-1)+.5;

y(a)=0.5*y(a-1);

end

end

plot(x,y,’o’)

title(‘Sierpinski’s triangle’)

legend(sprintf(‘N=%d Iterations’,N))

**Fractal tree**

```
```

`function treemain`

tic

clear all;

depth = 7;

figure 1;

hold on;

drawTree2(0, 0, 90, depth);

toc;

endfunction

function drawTree2(x1, y1, angle, depth)

deg_to_rad = pi / 180.0;

rot=30; #degrees :: rotation from second iteration

branchLength=100*depth;

if (depth != 0)

x2 = x1 + cos(angle * deg_to_rad) * branchLength;

y2 = y1 + sin(angle * deg_to_rad) * branchLength ;

line([x1, x2], [y1, y2],’LineWidth’,depth);

drawTree2(x2, y2, angle – rot, depth – 1);

drawTree2(x2, y2, angle + rot, depth – 1);

endif

endfunction

A note on fractal (from HH Hardey):

There are upper and lower limits to describe natural objects by fractals. A figure may look like a fern leaf, but continued generation of the “leaf on larger and larger scales produces only a larger and larger fern leaf. A fern “plant” will never be produced. Similarly, there is a smallest scale to which a fractal description applies. As the overall fern leaf pattern is repeated on smaller and smaller scales, eventually the scale of a single fern plant cell will be reached. A single cell does not look like the overall shape.