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	Mathematik-Online-Aufgabensammlung: Lösung zu
	Aufgabe 1514: Darstellung der Kochschen Schneeflocke

function p = snow_flake(steps)

% function q = snow_flake(steps)
% generates the polygon q of the Koch snow flake 

if nargin < 1; 
   steps = 3;
end;

% initial polygon and mask for subdivision
p = [0 1 1/2; 0 0 sqrt(3)/2];
mask = [0 0; 0 0; 1/3 0; 0 1/3; 1/2 sqrt(3)/6; ... 
   -sqrt(3)/6 1/2; 2/3 0; 0 2/3];
n = size(mask,1)/2;

% subdivision of edges 
% p(:,k), p(:,k+1) = p(:,k) + d(:,k)   
% mask(c:2:end,:)*d(:,k) yields 
% x- (c=1) and y-coordinates (c=2)
for k=1:steps;
   d = diff([p p(:,1)]')';
   p = repmat(p,n,1);
   p = mask*d+p;
   p = reshape(p,2,length(p(:))/2);
end;

% plot polygon
fill(p(1,:),p(2,:),[1 1 1]/2);
axis square;