# Construção da curva que preenche Sierpinski.

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

Sierpinski<-function(x,y,m){ # Replicação da iteração base.
z=matrix(c(x,y),2,2)
for ( i in 1:m){
q=matrix(0,2,3*length(z[1,])-2)
for (j in 1:(length(z[1,])-1)){
q[,(3*j-2):(3*j+1)]=it(z[,j:(j+1)],sinal);sinal=-sinal}
z=q};z
}


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

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

z=it(z,sinal);z
plot(z[1,],z[2,],'l',col="yellow")

z=Sierpinski(x,y,2)
plot(z[1,],z[2,],'l',col="blue")

z=Sierpinski(x,y,3)
plot(z[1,],z[2,],'l',col="green")


z=Sierpinski(x,y,8)
plot(z[1,],z[2,],'l',col="red")