### Recent Posts

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##### Fractal Image of the Month / Re: Fractal image of the month - Discussion thread
« Last post by ThunderboltPagoda on Today at 01:01:15 PM »
Where are the votes for the theme contest?

According to the number of gold medals, there are 14 votes for the normal contest at the moment, but only 2 (including mine from just before) for the theme contest. Hey people, you don't have to wait until there is "Please vote!" in the subject of the thread ...
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##### Fractal Mathematics And New Theories / Re: Plane filling Julia sets
« Last post by gerrit on Today at 08:54:52 AM »
Finding these space filling J sets is not hard manually.
Here I tried looking at parameter space image of $$(z^3 +2az^2 -z -1)/(z^3-7az^2 + az +1)$$ (typed in randomly) following the $$\infty$$ critical orbit with a the pixel parameter.
See image 1, then zoom in to a randomy looking region (im2) and get the Julia set for $$a=4.065453797 + 0.895652517 i$$. To check it's infinite I apply 1/z to my pixels to get an image centered on the other side of that Riemann sphere and zoom until I run out of precision/time to verify there is no hole (meaning a big but not infinite set). That's image 3.

How to find pretty ones is another matter...
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##### Fractal Mathematics And New Theories / Re: Kompassbrot uses and transcendental functions?
« Last post by gerrit on Today at 08:46:14 AM »
I told you that kompassbrot is cubic Mandelbrot fc(z)=z^3+k*z^2+Kn(k) where Kn(k) is Kompassbrot kind (n) as complex function.
K1(k)=(-2*k^3-9*k)/27  [Kompassbrot kind 1], at other kinds I yet don't know .
At each cubic Mandelbrots based by z^3+k*z^2+c, the Kn(k) are the point where bulbs or antenas has simetry, like in my picture with cubic mandelbrot based by z^3+2,5*z^2+c where I marked with yellow the points of Kompassbrot kind 2.

The kind of Kompassbrot is stabilised by the kind of bulbs whick has simetry (complex square collisions).

Kompassbrot kind 2 handmade look so:
Thanks for explaining.

Do I understand correctly that you mean the parameter space image of $$z^3+kz^2+F(k)$$, following some critical orbit (which?) with k the parameter (pixel), and F(k) a function you get somehow from parameter space image of $$z^3 + kz^2+c$$ with k now a constant and c (pixel) the parameter?
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##### Image Threads / Re: Asymmetrical
« Last post by pauldelbrot on Today at 08:18:35 AM »
Sparkler
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##### Fractal Mathematics And New Theories / Re: Kompassbrot uses and transcendental functions?
« Last post by hgjf2 on Today at 07:32:46 AM »
What is a "Kompassbrot"?
I told you that kompassbrot is cubic Mandelbrot fc(z)=z^3+k*z^2+Kn(k) where Kn(k) is Kompassbrot kind (n) as complex function.
K1(k)=(-2*k^3-9*k)/27  [Kompassbrot kind 1], at other kinds I yet don't know .
At each cubic Mandelbrots based by z^3+k*z^2+c, the Kn(k) are the point where bulbs or antenas has simetry, like in my picture with cubic mandelbrot based by z^3+2,5*z^2+c where I marked with yellow the points of Kompassbrot kind 2.

The kind of Kompassbrot is stabilised by the kind of bulbs whick has simetry (complex square collisions).

Kompassbrot kind 2 handmade look so:
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##### Fractal Mathematics And New Theories / Re: Plane filling Julia sets
« Last post by gerrit on Today at 07:04:22 AM »
Hi,
Here are the values of c that I was able to compute.
Very nice, it'll take me a while to try all those values.
Actually, in UF I can hover over the parameter space image and see the J-set in another window. The infinite ones all look pretty much the same to me. Wonder how you can get different ones.

I guess problem is that for more complicated rational functions the critical points will also depend on the parameters that you are solving for for Misiurewicz points and you get some complicated coupled polynomial equations that I can't quite see how to approach.
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##### Fractal movie gallery / Re: New Computer, more rendering power
« Last post by Tas_mania on Today at 05:50:08 AM »
Quote
I have been using MathMap forever because the x,y → rgba idiom does not have any preconceptions

I think 3D fractal software uses an x,y,z paradigm but I'm not sure what kind of maths engine is behind Mandelbulber or Fragmentarium.
I know some of the stuff I made with MathMap Composer looked 3D because it was based on 3D images that were processed by filter chains.

Quote
wishing for a GPU backend for MathMap
I've thought about that. Given it's a Gimp plugin and Gimp 10 has OpenCL as an option it should work but I don't think Gimp's OpenCL even works

I know Mark wanted you to maintain MathMap. I think you are in the right forum here. I started with Xaos but now mostly use Mandelbulber because it's under active development. Then so is Fragmentarium. I know there are very clever people here. I'm just an old guy (retired) on the other side of the Earth but the wildlife down here is quite amazing.
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##### Fractal Mathematics And New Theories / Re: Kompassbrot uses and transcendental functions?
« Last post by 3DickUlus on Today at 03:25:29 AM »

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##### Fragmentarium / Re: importing arbitarary channels from EXR files
« Last post by 3DickUlus on Today at 01:08:49 AM »
just putting together a commit for Development branch...

here's what I've got so far...

added optional channel spec to SamplerWidget
added optional channel spec to Parameters
reads and writes optional channel spec to settings
scans EXR file and creates channels pulldown
if user channel does not exist in file boarder of pulldown goes red

status: GUI only, I haven't coded any of the GL or special channel loading yet, just loads all channels as in default behavior

note: the channel spec can be adjusted to account for multiple channels or subset of All as a comma or semicolon separated list...
Code: [Select]
sampler2D varName; texture[ filename.exr, R;G;B ]At the stage now where this would be trivial to implement.

The only catch of course is that they actually have to exist, not sure yet how different format channels will work, float vs int, uint, half etc, I suppose OpenEXR can tell what format each channel is so will just have to add that and create the GL texture accordingly.

have a look, run from cmdline (no verbose) for some debug, outputting at where I left off...
Code: [Select]
"DisplayWidget.cpp" 728 loadEXRTexture Default:  "myTexture" "texture2.jpg" """DisplayWidget.cpp" 734 loadEXRTexture Requested:  "myTexture" "Ditch-River_2k.exr" "All""DisplayWidget.cpp" 1645 setShaderUniforms Setting: "myTexture" "Ditch-River_2k.exr" "All"
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##### Image Threads / Re: zm49 (Stars)
« Last post by CFJH on Yesterday at 11:30:46 PM »
16x4Stars (at E38995)
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