[]=koch(n)

%KOCH: Plots 'Koch Curve' Fractal
% 
% koch(n) plots the 'Koch Curve' Fractal after n iterations
% e.g koch(4) plots the Koch Curve after 4 iterations.
% (be patient for n>8, depending on Computer speed)
%
% The 'kline' local function generates the Koch Curve co-ordinates using
% recursive calls, while the 'plotline' local function is used to plot
% the Koch Curve.
%
% Copyright (c) 2000 by Salman Durrani ([e-mail])
%--------------------------------------------------------------------
function []=koch(n)
global X1 Y1 X5 Y5 i
if (n==0)
   x=[0;1];
   y=[0;0];
   line(x,y,'Color','b');
   axis equal
   set(gca,'Visible','off')
else
   levelcontrol=10^n;
   L=levelcontrol/(3^n);  
   l=ceil(L);
   kline(0,0,levelcontrol,0,l);
   axis equal
   set(gca,'Visible','off')
   set(gcf,'Name','Koch Curve')
end
%--------------------------------------------------------------------
function kline(x1,y1,x5,y5,limit)   
global X1 Y1 X5 Y5 i
length=sqrt((x5-x1)^2+(y5-y1)^2); 
if(length>limit)
   x2=(2*x1+x5)/3;
   y2=(2*y1+y5)/3;
   x3=(x1+x5)/2-(y5-y1)/(2.0*sqrt(3.0));
   y3=(y1+y5)/2+(x5-x1)/(2.0*sqrt(3.0));
   x4=(2*x5+x1)/3;
   y4=(2*y5+y1)/3;
   % recursive calls
   kline(x1,y1,x2,y2,limit);
   kline(x2,y2,x3,y3,limit);
   kline(x3,y3,x4,y4,limit);
   kline(x4,y4,x5,y5,limit);
else 
   plotline(x1,y1,x5,y5); 
end
%--------------------------------------------------------------------
function plotline(a1,b1,a2,b2)
global X1 Y1 X5 Y5 i
x=[a1;a2];
y=[b1;b2];
X1(i)=a1;Y1(i)=b1;X5(i)=a2;Y5(i)=b2;i=i+1;
%pause
line(x,y);
%--------------------------------------------------------------------