I attached a few random fractals to improvisation videos. For that, I chose fractal plots that remind of astronomical images:
http://www.youtube.com/watch?v=H9bqspaQ84g&feature=related
http://www.youtube.com/watch?v=YYKLfx7e7tU&NR=1
Monday, April 11, 2011
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)
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)
Wednesday, April 25, 2007
Fractal interpolation
Iterated function system for fractal interpolation. Copy-paste and run.
http://users.utu.fi/attenka/FractInterpolation.R
http://users.utu.fi/attenka/FractInterpolation.R
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
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
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
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)
####################
#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)
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