## Monday, April 11, 2011

### Some random fractals

I attached a few random fractals to improvisation videos. For that, I chose fractal plots that remind of astronomical images:

## Thursday, November 22, 2007

### Wallpaper attractor

Hello,

Here is again a nice code
from Bernardo Rangel Tura.
#
# Wallpaper
#
#xn+1 = yn - sign(xn) | b xn - c |1/2
#yn+1 = a - xn
#
# a=1
# b=4
# c=60

wallpaper<-function(n=4E4,x0=1,y0=1,a=1,b=4,c=60){
x<-c(x0,rep(NA,n-1))
y<-c(y0,rep(NA,n-1))
cor<-rep(0,n)

for (i in 2:n){

x[i] = y[i-1] - sign(x[i-1])*sqrt(abs( b*x[i-1] - c) )
y[i] = a - x[i-1]
cor[i]<-round(sqrt((x[i]-x[i-1])^2+(y[i]-y[i-1])^2),0)
}
n.c<-length(unique(cor))
cores<-heat.colors(n.c)

plot(x,y,pch=".",col=cores[cor])

}

wallpaper()

"In this code I colored points based in velocity ..." (B.R. Tura)

## Saturday, April 21, 2007

### Julia and Mandelbrot

I made a video using the developed versions of the codes presented below. The quality of the video is fairly poor but the idea becomes clear. The function, which forms the successive julia sets is C=a+sin(3*a)i, (-1.5 < a < 0.5), in which C is a complex parameter for the julia set.

http://www.ag.fimug.fi/~Atte/Julia&Mandelbrot.wmv

http://www.ag.fimug.fi/~Atte/Julia&Mandelbrot.rm

## Wednesday, April 18, 2007

### Mandelbrot set

Very inefficient code. Takes a few minutes to compute depending on the processor speed...

http://users.utu.fi/attenka/mandelbrot_set.R

### Julia set

Perhaps not the most powerful code (you have to wait a little...) but readable and it works.

http://users.utu.fi/attenka/julia_set.R ## Monday, April 16, 2007

### Rossler Attractor

Another code from Bernardo Rangel Tura. Thank you!

####################
#Rossler Attractor #
####################

#dx / dt = - y - z
#dy / dt = x + a y
#dz / dt = b + z ( x - c )
#
#where a = 0.2, b = 0.2, c = 5.7

rossler<-function(n=2000,a=.2,b=.2,c=1.7,x0=0.0001,y0=0.0001,z0=0.0001){
x<-c(x0,rep(NA,n-1))
y<-c(y0,rep(NA,n-1))
z<-c(z0,rep(NA,n-1))
h<-0.015
for (i in 2:n){
x[i]<-x[i-1]-h*(y[i-1]+z[i-1])
y[i]<-y[i-1]+h*(x[i-1]+a*y[i-1])
z[i]<-z[i-1]+h*(b+z[i-1]*(x[i-1]-c))
}
require(rgl)
rgl.clear()
rgl.points(x,y,z, color=heat.colors(n), size=1)
}

rossler(2000,x0=3,y0=4,z0=.4)