### Variations on a theme by gerrit

• 75 Replies
• 2448 Views

0 Members and 1 Guest are viewing this topic.

#### gerson

• Fractal Frogurt
• Posts: 432

#### Re: Variations on a theme by gerrit

« 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.

• 3f
• Posts: 1820

#### Re: Variations on a theme by gerrit

« 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?

• 3c
• Posts: 839

#### Re: Variations on a theme by gerrit

« 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?

#### gerson

• Fractal Frogurt
• Posts: 432

#### Re: Variations on a theme by gerrit

« 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

• 3f
• Posts: 1820

#### Re: Variations on a theme by gerrit

« 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

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

#### Spyke

• Strange Attractor
• Posts: 98

#### Re: Variations on a theme by gerrit

« 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.
Earl Hinrichs, offering free opinions on everything.

#### gerson

• Fractal Frogurt
• Posts: 432

#### Re: Variations on a theme by gerrit

« 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 »

• 3f
• Posts: 2244

#### Re: Variations on a theme by gerrit

« 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.

• 3f
• Posts: 2244

#### Re: Variations on a theme by gerrit

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

• 3f
• Posts: 2244

#### Re: Variations on a theme by gerrit

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

#### gerson

• Fractal Frogurt
• Posts: 432

#### Re: Variations on a theme by gerrit

« 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.

• 3f
• Posts: 2244

#### Re: Variations on a theme by gerrit

« 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.

• 3f
• Posts: 2244

#### Re: Variations on a theme by gerrit

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

#### gerson

• Fractal Frogurt
• Posts: 432

#### Re: Variations on a theme by gerrit

« 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

• 3f
• Posts: 2244

#### Re: Variations on a theme by gerrit

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

### Similar Topics

###### Fractal Theme contest -July 2020 Theme is: 'Fire and Ice' The winners are?

Started by Caleidoscope on Fractal Image of the Month

16 Replies
624 Views
July 29, 2020, 11:04:03 AM
by Caleidoscope
###### Fractal Theme IOTMC, August 2020 - Theme is space! The winners are?

Started by Caleidoscope on Fractal Image of the Month

13 Replies
525 Views
August 28, 2020, 06:34:14 PM
by Caleidoscope
###### Fractal Theme contest -June 2020 Theme is: 'is this Art'? And the winners are?

Started by Caleidoscope on Fractal Image of the Month

21 Replies
858 Views
June 29, 2020, 09:58:30 AM
by Caleidoscope
###### Theme contest February-2020 Theme is Garden. The winners are?

Started by Caleidoscope on Fractal Image of the Month

13 Replies
694 Views
February 28, 2020, 08:42:00 PM
by Caleidoscope
###### Fractal Theme IOTMC May 2020, Theme is 'Architecture' And the winners are?

Started by Caleidoscope on Fractal Image of the Month

14 Replies
614 Views
May 29, 2020, 07:15:40 PM
by Sabine62