Re: [R] Fractals with R
Now problems with plot-command...
I try to plot Julia set and the algorithm works, if the points are drawn during
the loop. But if I want to save the values first to the matrix and then
afterwards plot them at once, the picture is distorted. What's wrong with the
plot-command? I think the PointsMatrix is ok?
-Atte
C=-0.7-0.4i # Complex parameter, connected to coordinate of the Mandelbrot set
in a complex plane.
Limits=c(-2,2)
z=0+0i
MaxIter=60
cl=colours()
Step=seq(Limits[1],Limits[2],by=0.01)
PointsMatrix=array(0,dim=c(length(Step)*length(Step),3))
a1=0
for(x in Step)
{
for(y in Step)
{
z1=x+y*1i
n=0
z=z1
while(nMaxIter abs(z)2)
{
z=z^2+C
n=n+1
}
if(abs(z)2) colour=1
else colour=n*10
#points(z1, pch=., col=cl[colour]) # This works!
# But this doesn't!
a1=a1+1
PointsMatrix[a1,]=c(x,y,colour)
}
}
#???
plot(PointsMatrix[,1], PointsMatrix[,2], xlim=Limits, ylim=Limits,
col=cl[PointsMatrix[,3]], pch=.)
##
Atte Tenkanen wrote:
Hi,
That is of counter for web page. Do you get some pop-up windows?
Atte
Hi Atte,
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Re: [R] Fractals with R
Here is a workable version for the Julia set. I put it also to
http://fractalswithr.blogspot.com/
Atte
Now problems with plot-command...
I try to plot Julia set and the algorithm works, if the points are
drawn during the loop. But if I want to save the values first to
the matrix and then afterwards plot them at once, the picture is
distorted. What's wrong with the plot-command? I think the
PointsMatrix is ok?
-Atte
C=-0.7-0.4i # Complex parameter, connected to coordinate of the
Mandelbrot set in a complex plane.
Limits=c(-2,2)
z=0+0i
MaxIter=60
cl=colours()
Step=seq(Limits[1],Limits[2],by=0.01)
PointsMatrix=array(0,dim=c(length(Step)*length(Step),3))
a1=0
for(x in Step)
{
for(y in Step)
{
z1=x+y*1i
n=0
z=z1
while(nMaxIter abs(z)2)
{
z=z^2+C
n=n+1
}
if(abs(z)2) colour=1
else colour=n*10
#points(z1, pch=., col=cl[colour]) # This works!
# But this doesn't!
a1=a1+1
PointsMatrix[a1,]=c(x,y,colour)
}
}
#???
plot(PointsMatrix[,1], PointsMatrix[,2], xlim=Limits, ylim=Limits,
col=cl[PointsMatrix[,3]], pch=.)
#---
-#
Atte Tenkanen wrote:
Hi,
That is of counter for web page. Do you get some pop-up windows?
Atte
Hi Atte,
__
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
[R] Fractals with R
Hi everybody, I put some R-code to a web page for drawing fractals. See http://fractalswithr.blogspot.com/ If you have some R-code for fractal images, I'm willing to include them to the page. Has somebody tried L-systems or Markov algorithm (http:// en.wikipedia.org/wiki/Markov_algorithm) with R? Best wishes, Atte Tenkanen University of Turku, Finland __ [EMAIL PROTECTED] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Fractals with R
kone wrote: Hi everybody, I put some R-code to a web page for drawing fractals. See http://fractalswithr.blogspot.com/ If you have some R-code for fractal images, I'm willing to include them to the page. That's really nice, but what's with the annoying popups, courtesy of Webstats4U? Gad -- Gad Abraham Department of Mathematics and Statistics The University of Melbourne Parkville 3010, Victoria, Australia email: [EMAIL PROTECTED] web: http://www.ms.unimelb.edu.au/~gabraham __ [EMAIL PROTECTED] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Fractals with R
Hi, That is of counter for web page. Do you get some pop-up windows? Atte kone wrote: Hi everybody, I put some R-code to a web page for drawing fractals. See http://fractalswithr.blogspot.com/ If you have some R-code for fractal images, I'm willing to include them to the page. That's really nice, but what's with the annoying popups, courtesy of Webstats4U? Gad -- Gad Abraham Department of Mathematics and Statistics The University of Melbourne Parkville 3010, Victoria, Australia email: [EMAIL PROTECTED] web: http://www.ms.unimelb.edu.au/~gabraham __ [EMAIL PROTECTED] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Fractals with R
Atte Tenkanen wrote: Hi, That is of counter for web page. Do you get some pop-up windows? Atte Hi Atte, Yes, annoying stuff from http://ilead.itrack.it. Your webcounter provider using their scripts to do this, without your intervention. How nice of them... Cheers, Gad -- Gad Abraham Department of Mathematics and Statistics University of Melbourne Victoria 3010, Australia email: [EMAIL PROTECTED] web: http://www.ms.unimelb.edu.au/~gabraham __ [EMAIL PROTECTED] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Fractals with R
kone wrote: Hi everybody, I put some R-code to a web page for drawing fractals. See http://fractalswithr.blogspot.com/ If you have some R-code for fractal images, I'm willing to include them to the page. Has somebody tried L-systems or Markov algorithm (http:// en.wikipedia.org/wiki/Markov_algorithm) with R? Here's an interactive example of how to draw pretty pictures with polynomials and other R functions: http://biostat3.mc.vanderbilt.edu/polyart/ ...without the pop-up windows ;) Cheers, Jeff -- http://biostat.mc.vanderbilt.edu/JeffreyHorner __ [EMAIL PROTECTED] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Fractals with R
Hi Jeff, Thank you for the nice page. I also have done some R-videos combining jpeg's in video editor (or with mjpegtools) but this kind of command in R would be useful. Unfortunately I couldn't install NRart-package but got a lot of fun when playing with your Start Making Art!-page. I haven't met pop-ups in my page, but perhaps the counter-server detects my id and leave me alone? Atte kone wrote: Hi everybody, I put some R-code to a web page for drawing fractals. See http://fractalswithr.blogspot.com/ If you have some R-code for fractal images, I'm willing to include them to the page. Has somebody tried L-systems or Markov algorithm (http:// en.wikipedia.org/wiki/Markov_algorithm) with R? Here's an interactive example of how to draw pretty pictures with polynomials and other R functions: http://biostat3.mc.vanderbilt.edu/polyart/ ...without the pop-up windows ;) Cheers, Jeff -- http://biostat.mc.vanderbilt.edu/JeffreyHorner __ [EMAIL PROTECTED] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Fractals in R and having fun! (and more persp and color)
Hi Martin, Thanks a lot for pointing your function out to me. I tried it, and indeed it is very fast. I will have a close look at the asymmetry problem in my own code, although this sounds pretty bizarre to me, I mean, I realised that there was some asymmetry but I didn't really payed attention to that. I think that the high number of iterations that can be achieved with your function will be the solution to obtaining 'smoother' slopes in the perspective plot (i.e. the outer regions that rise progressively towards the set). If you come with any ideas on how to improve that perspective let me know. I think I'll have a go to the c code. Thanks, Mario. At 10:21 18/09/03 +0200, you wrote: Mario Well, I started playing with fractals in R, and wrote Mario a function to generate de Mandelbrot set, which might Mario be of interest to some people Mario ### Mario # Mandelbrot set Mario ### Mario mandelbrot - function(x = c(-3.0, 1.0), # x coordinates Marioy = c(-1.8, 1.8), # y coordinates Mariob = .05,# by 'steps' Marioiter = 20) # maximum number of iterations .. .. .. Well, only a bit more than year ago I had posted my version of mandelbrot() and a drawing function, see http://finzi.psych.upenn.edu/R/Rhelp02a/archive/5898.html [ I have a slightly updated version of the R code, that is now available as ftp://stat.ethz.ch/U/maechler/R/Mandelbrot.R ] which is an order of magnitude more efficient than yours (22 x faster for your b = 0.01, *1), *2) and with an iterImage() function for drawing its result in several (simple) color schemes. I agree that the proper solution would *definitely* use C code! Your idea of using persp() -- while seen frequently in fractal books, is new ``for R'' however, and nice! Thank you. Regards, Martin *1) mainly because I only have the iteration loop and do the rest vectorized, but also because I have a check for symmetry and make use of it when appropriate *2) For speed comparison, note that I use 10 x more iterations and a much higher resolution by default *3) When I do the comparison, I see that your function's result slightly differs from mine -- not for the Mandelbrot set itself, but for the very ``outer points'' (the dark orange ones in the image plot). Your result is asymmetric and hence can't be quite correct. __ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
[R] Fractals in R and having fun! (and more persp and color)
Well, I started playing with fractals in R, and wrote a function to
generate de Mandelbrot set, which might
be of interest to some people
###
# Mandelbrot set
###
mandelbrot - function(x = c(-3.0, 1.0), # x coordinates
y = c(-1.8, 1.8), # y coordinates
b = .05,# by 'steps'
iter = 20) # maximum number of iterations
{
m = NULL # will store the results, this is the 'image' matrix
for(i in seq(x[1], x[2], by = b)) {
r = NULL # stores part of the iteration results
for(j in seq(y[1], y[2], by = b)) {
it = iter # will hold iteration at which point (i, j) breaks off
c = c(i, j) # initial point
z = c(i, j) # i: real part; j: imaginary part
for(k in 1:iter) {
# the Mandelbrot iteration formulae: z - z*z + c
z = c(z[1]^2 - z[2]^2, 2 * z[1]*z[2]) + c
# tests if point breaks off
if((z[1] + z[2])^2 4) { it = k; break }
}
r = c(r, it) # stores iteration results
}
# constructs the 'image' matrix
m = rbind(m, r)
}
# the output fractal object
fractal = list(x = seq(x[1], x[2], by = b), # x coordinates
y = seq(y[1], y[2], by = b), # y coordinates
z = m)# it matrix
}
##
# here goes how it works
##
frac - mandelbrot()
image(frac) # perhaps not very nice!
# more resolution, beware, this might take some time to calculate
frac - mandelbrot(b = .01)
image(frac)
# now here comes the fun, lets do a persp plot of the set!
persp(log(frac$z), border = NA, theta = 225, phi = 45, col = gray, shade
= .4)
###END###
Well, here comes what would have been my question. How to put some nice
colors to the above perspective plot? I wanted to post this question some
weeks ago, but it was answered yesterday after all the discussion on persp
and colors. If you see my previous post, you'll the definition of
surf.colors used below:
persp(log(frac$z), border = NA, theta = 225, phi = 45, col =
surf.colors(frac$z, col = c(gray(seq(0.5, 1, len = 39)), black)), shade =
.4)
that was what I always wanted to do, and this was the source of my
confusion when checking the code in persp demo.
But now some new question arises, which I'll leave to the interested hacker:
Any C programmer who volunteers to write and link c code to R to calculate de
Mandelbrot set faster?
Does anyone have any idea on how to 'smooth' the valleys and ridges that
rise towards the set?, i.e. to avoid the stairs like appearence of the plot?
I hope you can have some fun with this!
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