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1
Image Threads / Re: gerrit images
« Last post by mrrudewords on Today at 12:45:30 PM »
\(
w_0 = 0\\
z_0 = c\\
q = 1/2\\
r = 10^{-6}\\
w \leftarrow qw/z + c\\
z \leftarrow  z^2 + rw^2 + c
 \)

This is super! I'm trying to code it but having trouble getting the same result. Would you be able to shed some light on what I'm doing wrong?

        // global
        double q = 0.5;
        double r = 10 ^ -6;

        // init pixel
        C = coordinates
        Z = coordinates
        W = Complex.Zero

        // iterate pixel
        W = Complex.Divide(Complex.Multiply(q, W), Complex.Add(Z, C));
        Z = Complex.Add(Complex.Add(Complex.Pow(Z, CalcPower), Complex.Pow(Complex.Multiply(r, W), CalcPower)), C);

        ( also tried W = Complex.Add(Complex.Divide(Complex.Multiply(q, W), Z), C); )
2
Forum Help And Support / Re: Pictures disappeared in the old forum
« Last post by Fraktalist on Today at 11:14:03 AM »
yep it does look very bad indeed.
I asked him to clean the logs 2days ago to help recurring, known issues caused by overflowing logs. that didn't help but seems to have made it worse.
I fear he has lost interest in spending time with it.

But not all is lost: we have a full backup of the archive and could restore it here (or better at .com, if Christian gives us access to the domain).
Problem is, that it will be a huge effort and take a lot of time, which we currently just don't have. But it's on our radar.

Regarding images here: I can assure you they are stored safely, backupped regularly and we will take care that everything stays online as long as we are able to maintain the site, hopefully infinity. (notice that sweet new donation button? ;))
3
Image Threads / Re: Experiments with colouring and layers
« Last post by Caleidoscope on Today at 11:04:56 AM »
Thanks. I'm glad you like them. I've become addicted to zooming and colouring so much that my family aren't sure if I'm sane  :yes:

:D  They gave up on me a long time ago ;)
4
Meet & Greet / Re: What's up Fractal Fans? - Australia!
« Last post by Caleidoscope on Today at 10:49:55 AM »
With a attitude like that, I'm sure you will  :)   Glad you joined!   :thumbs:
5
Fractal Mathematics And New Theories / Holomorphic Mandelbrot extensions
« Last post by gerrit on Today at 05:52:20 AM »
While the classical Mandelbrot set \( z \leftarrow z^2 +c \) remains the king of (2D) fractals, I'm interested in generalizations.
Personally I find all the non-holomorphic extensions like burning ship unappealing.

Extensions to  \( z \leftarrow f(z) +c \) with a holomorphic \( f \) include polynomials, rational functions, and entire functions.
Interesting to explore but in my experience they don't add that many new features when you start zooming, as you'll find mini M-sets with weird decorations, but not much more.

Recently pauldelbrot posted a formula based on two complex variables, "Mandelbrot foam", which I find extremely interesting in that it is really different from the M-set; no familiar patterns appear at all, yet it is not "ugly" like the non-holomorphic formulas (IMHO of course).

I'm interested in strategies to find such interesting fractals, but don't know how to approach it. Making tweaks to M-foam gave some interesting results, but how take a more mathematically informed approach?

For example, what is a "critical point" when you have multiple variables? Is it where the Jacobian is zero? Or just the determinant (local magnification)?

More generally, how do you come up with "interesting" formulas?

I realize my questions may not have a real (or complex :) answer but any ideas would be appreciated.

6
Image Threads / Re: gerrit images
« Last post by gerrit on Today at 04:39:04 AM »
\(
w_0 = 0\\
z_0 = c\\
q = 1/2\\
r = 10^{-6}\\
w \leftarrow qw/z + c\\
z \leftarrow  z^2 + rw^2 + c
 \)
7
if your card doesn't support at least GL4.1 and you don't have the OpenEXR libs installed then the nv-exr version is expected to fail.

there is a bool flag (checkbox) in some frags named "Depth to Alpha" that allows storing the depth values in the alpha channel of EXR formatted images, EXR also stores  values as float32 for higher dynamic range, these are the only features that using EXR contributes, not really required unless you want to do some heavy post processing after rendering.
8
Nice. I guess a better algorithm is better than a quantum computer.
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Forum Help And Support / Re: Pictures disappeared in the old forum
« Last post by 3DickUlus on Today at 01:21:48 AM »
it looks worse on my system, text only, no css?  :P   :'(
10
Not sure I'm getting this. AFAIK the "potential model" is an approximation of the Navier-Stokes equation, with limited applicability.
If there is turbulence you need full Navier-Stokes, but numerical solution is "impossible" due to cascade of vortices down to very small scale, requiring impractical small mesh units and timesteps.

You drew such an example with flow through a constriction and turbulence. Now where does the "fractal theory" come in, except in your title for the drawing?
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