####################
## MANDELBROT SET ##
####################

Limits=c(-2,0.8)
MaxIter=25
cl=colours()
Step=seq(Limits[1],Limits[2],by=0.005)
S=floor(length(cl)/MaxIter)
Dist=0
PointsMatrix=array(0,dim=c(length(Step)*length(Step),3))
t=0


for(a in Step)
{
	for(b in Step+0.6)
	{
		x=0;y=0;n=0;Dist=0
		while(n<MaxIter & Dist<4)
		{
			n=n+1
			newx=a+x^2-y^2
			newy=b+2*x*y
			Dist=newx^2+newy^2
			x=newx;y=newy
		}
		if(Dist<4) colour=24 # black colour
		else colour=n*S
		t=t+1
		PointsMatrix[t,]=c(a,b,colour)
	}
}

X11()

plot(PointsMatrix[,1], PointsMatrix[,2], xlim=Limits, ylim=Limits+0.6, col=cl[PointsMatrix[,3]], pch=".")