[1] Re: Function for Kochs snowflake
Date: Tue Jan 02 20:30:51 EST 2007
Lines: 89

e.g. see:
http://mathworld.wolfram.com/KochSnowflake.html

> Ken - that would be the best solution but I donīt have much time so
> Iīd hope somebody could guide me.
> 
>  Ken Davis wrote:
>>
>>
>> "Beginner" <partypingla@gmail.com> wrote in message
>> news:ef4a06b.-1@webcrossing.raydaftYaTP...
>>> Hi,
>>> I'm new on using Matlab and I could need some help.
>>> I want to create a picture of Kochs snowflake but I donīt know
>> how.
>>> Unforturnatly I dont even got a clue where to begin.
>>> Can somebody help me
>>> If you got time Iīd be grateful for stepbystep instructions

Okay Beginner, I will give you a start.

As you know, the Koch snowflake starts from a triangle. We will parameterize
this by a relative angle variable and a unit length l:

angle = [0, -2/3*pi, -2/3*pi];
l = 1;

which can be visualized as follows:

x = zeros([length(angle)+1, 1]);
y = zeros([length(angle)+1, 1]);

x(1) = 0; y(1) = 0; 
phi=0;
for i=1:length(angle);
    phi = phi+angle(i);
    x(i+1) = x(i) + l * cos(phi);
    y(i+1) = y(i) + l * sin(phi);
end

plot(x,y);
axis tight equal;

This displays the basic shape. The thing you need to realize now is that the
generator for the Koch snowflake in terms of the relative angle is 

phi -> [phi, pi/3,-2*pi/3, pi/3] for each phi in angle;
l -> l /3;

That is, at each refinement of the curve, the angle array increases by a
factor 4 and the length parameter l shrinks by a factor 3.

Here is the entire code (iters is the number of times you would like to
refine the shape - do not set iters very high as the length of angle goes
as 4^iters !!!!):

angle = [0, -2/3*pi, -2/3*pi];
l = 1;
iters=0;

for i=1:iters
    l = l/3;
    angle1 = zeros([4*length(angle),1]);
    for j=1:length(angle)
      % insert the Koch generator here
    end
    angle = angle1;
end

x = zeros([length(angle)+1, 1]);
y = zeros([length(angle)+1, 1]);

x(1) = 0; y(1) = 0; 
phi=0;
for i=1:length(angle);
    phi = phi+angle(i);
    x(i+1) = x(i) + l * cos(phi);
    y(i+1) = y(i) + l * sin(phi);
end

plot(x,y);
axis tight equal;

You only need to add one line of code to make it work! Good luck,

Maarten

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