分形的练习一

①Koch曲线

用复数的方法来迭代Koch曲线

clear i 防止i被重新赋值

A=[0 1] 初始A是连接（0，0）与（1，0）的线段

t=exp(i*pi/3)

n=2 n是迭代次数

for j=0:n

A=A/3 a=ones(1,2*4^j)

A=[A (t*A+a/3) (A/t+(1/2+sqrt(3)/6*i)*a) A+2/3*a]

end

plot(real(A),imag(A))

axis([0 1 -0.1 0.8])



②Sierpinski三角形

A=[0 1 0.5 0 0 1] 初始化A

n=3 迭代次数

for i=1:n

A=A/2 b=zeros(1,3^i) c=ones(1,3^i)/2

A=[A A+[c b] A+[c/2 c]]

end

for i=1:3^n

patch(A(1,3*i-2:3*i),A(2,3*i-2:3*i), b ) patch填充函数

end

-Fractal

Exercise One

The ① Koch curve

Plural iteration Koch curve

clear i　 to prevent i is reassigned

A = [0 1]　 initial A is a connection (0,0) and (1,0) of the segments

t = exp (i* pi/3)

n = 2　 n is the number of iterations

for j = 0: n

A = A/3　a = ones (1,2* 4 ^ j)

A = [A (t* A+ a/3) (A/t+ (1/2+ sqrt (3)/6* i)* a) A+2/3* a]

end

plot (real (A), imag (A))

axis ([0 1-0.1 0.8])

 

② Sierpinski triangle

A = [0 1 0.5　0 0 1]　 initialized A

n = 3　 the number of iterations.

for i = 1: n

A = A/2　b = zeros (1,3 ^ i)　c = ones (1,3 ^ i)/2

A = [A A+ [c　b] A+ [c/2　c]]

end

for i = 1:3 ^ n

patch (A (1,3* i-2: 3* i), A (2,3* i-2: 3* i),　b )　 patch filled function

end