Variations on a theme by gerrit

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Offline gerson

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« Reply #60 on: May 29, 2019, 07:35:19 PM »
@Spyke Reply #54 use Maximum iteration's in coloring method.
Thanks gerrit, Spyke and mrrudewords for help. Is hard to me understand all this math and code, but I am having a lot of fun playing with this formulas including julia's one.
I am posting other imagem with bailout 10000, as the others I posted it doesn't show that minibrot below the triangle as appears in first post, Reply # 2, 13 and 44.

Offline 3DickUlus

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« Reply #61 on: May 30, 2019, 01:56:57 AM »
I think I know why it doesn't show the minibrot, but I would have to see the source code, is this an opensource project? github?

Offline marcm200

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« Reply #62 on: May 31, 2019, 07:07:44 AM »
@gerson: I haven't implemented that function specifically, but when I was trying to recreate pauldelbrot's fractured mirror image, I couldn't find that metallic minibrot at first either. For me, the solution was the max iteration count. I used only 1000 at first, but only after I increased to 100,000 the minibrot started to appear (the coloring method was dependent on very many iterations). Maybe yours is appearing as well only in a specific iteration number window?

Offline gerson

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« Reply #63 on: May 31, 2019, 07:21:59 PM »
@  3DickUlus
Fractal Zoomer let to program in colors using Edit User Code in User In Coloring Method's window. Is a Java file that use that multiple argument user functions (see last image abouve). But I don't know how to code it very well.
https://sourceforge.net/projects/fractalzoomer/files/src/
https://en.wikibooks.org/wiki/Fractals/fractalzoomer

Offline 3DickUlus

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« Reply #64 on: June 01, 2019, 02:24:57 AM »
wow, that's a lot of code for someone that doesn't code very well  :thumbs:

initialize
A = (3.0,3.0) B = (1.0,0.0)
z = (0.0,0.0) and C = (X,Y)

 then iterate z = ( z^2 +A / z^2 +B ) +C

my frag code did the same thing, no mini, because z was not initialized to 0

Offline Spyke

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« Reply #65 on: June 02, 2019, 03:54:11 PM »
That makes a lot of sense. The triangle will look almost the same with any starting point. But the mini starts to decay, and soon disappears when you move off the critical point.
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Offline gerson

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« Reply #66 on: June 03, 2019, 07:24:28 PM »
@  3DickUlus Oh, no, that code was made by superheal (Fractal Zoomer programmer). See:
https://fractalforums.org/other/55/fractal-zoomer/2507
I just do some basic code into its "Edit User Code" file and after I compile it using Compile User Code button.
Edit User Code is a text file saved as .java that one can code.
I use m1(z, c, v1,v2,v3,v4) to call this code on that file and choose a User in coloring method (in = norm(sin(z)) * 100) to get the image attatched.
Now I got the minibrot. Thanks for the tip.

   public static Complex m1(Complex z, Complex c, Complex w, Complex n, Complex q, Complex r, Complex z7, Complex z8, Complex z9, Complex z10) {
   
      if(n.getRe() == 0) { // on the first iteration assign the initial value, z is already set to c

         w.assign(new Complex(3, 3)); // w = (3+3i);
         r.assign(new Complex(1, 0)); // r = (1+0i);
         z.assign(new Complex(0, 0)); // z = 0;
      }
         n.assign(z.square().plus(w)); // n = (z^2+w)
         q.assign(z.square().plus(r)); // q= (z^2+q)
   
      
      return (n.divide(q).plus(c)); // the return value is always assigned to z, which means z = n/q +c = ( z^2 +A / z^2 +B ) +C
   
   }
« Last Edit: June 03, 2019, 09:10:12 PM by gerson »

Offline gerrit

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« Reply #67 on: July 15, 2019, 11:01:09 PM »
\( \frac{z^2+1+i}{z^3+1} + c \).
Looks like it's photoshopped but the cloudyness comes from the fractal.

Offline gerrit

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« Reply #68 on: July 17, 2019, 08:02:58 AM »
\( \frac{z^2+1/2}{z^3+1} + c \).

Offline gerrit

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« Reply #69 on: July 19, 2019, 04:12:47 AM »
\( \frac{z^2}{z^2+1} + c \).

Offline gerson

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« Reply #70 on: July 19, 2019, 06:54:27 PM »
Amazing image, is it a julia? This formula give good results.
Could you post the coordinates? is necessary to put z0=0 too? I will try to do it with Fractal Zoomer.

Offline gerrit

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« Reply #71 on: July 19, 2019, 11:31:17 PM »
Amazing image, is it a julia? This formula give good results.
Could you post the coordinates? is necessary to put z0=0 too? I will try to do it with Fractal Zoomer.
x = -0.9979713704745
y= 1.18482876902
Magn 38.861346

Parameter space image. I used critical point z=0. If you use other critical point \( z_0=\infty \) (implemented as \( z_0=1+c \)) the red ocean is the same, but the sky is just empty blue.

Offline gerrit

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« Reply #72 on: July 19, 2019, 11:32:44 PM »
\( \frac{z^2}{z^2+0.1} + c \).

Offline gerson

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« Reply #73 on: July 20, 2019, 12:00:20 AM »
thanks, I will try next weekend.
See what I got with Reply #69 formula.
orbit trap with Bailout 1000

Offline gerrit

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« Reply #74 on: July 20, 2019, 12:34:56 AM »