# Construção da curva de Koch.

it <- function(z){ # Iteração base
p=matrix(0,2,5);u=z[,2]-z[,1]; t=pi/3
M=matrix(c(cos(t),sin(t),-sin(t),cos(t)),2,2)
p[,1]=z[,1];p[,2]=z[,1]+u/3 
p[,3]=p[,2]+M%*%(u/3);p[,4]=z[,2]-u/3; p[,5]=z[,2];p}

SnowFlake<-function(x,y,m){ # Replicação da iteração base.
t=pi/3
M=matrix(c(cos(t),sin(t),-sin(t),cos(t)),2,2)
z=matrix(c(x,x+M%*%(y-x),y,x),2,4)
for ( i in 1:m){
q=matrix(0,2,4*length(z[1,])-3)
for (j in 1:(length(z[1,])-1)){
q[,(4*j-3):(4*(j+1)-3)]=it(z[,j:(j+1)])}
z=q};z
}


# --- Teste -----------------------------------

x=c(0,1)
y=c(1,2)
z=matrix(c(x,y),2,2)
plot(x,y,'l') # Teste

z=it(z);z
plot(z[1,],z[2,],'l')


z=SnowFlake(x,y,6);
plot(z[1,],z[2,],'l',axes=FALSE,col="red")