• August 02, 2021, 08:45:57 AM

### Author Topic:  Kalles Fraktaler 2.15  (Read 10541 times)

shapeweaver and 1 Guest are viewing this topic.

#### Alef

• Fractal Furball
• Posts: 248
• a catalisator / z=z*sinh(z)-c^2
##### Re: Kalles Fraktaler 2.15
« Reply #240 on: June 21, 2021, 02:21:50 AM »
z→z^n *|z|^b+c (by gerrit)
Animation of the 3rd with the b factor varying from about -0.4 to +0.4 and back, with power n = 2 regular part.
It reminds me mandelbrot with unit vector addition:
z= z^2 + c
z = z + n* z/|z|
But it certainly is different (no holes?), maybe better (or maybe just images are good;) ).
Mandelbrot with unit vector made good results mosly with small negative n say n= -0.2 thus generating circles. Or maybe it is same, or maybe it is subset of Gerrit's formula? http://www.fractalforums.com/mandelbrot-and-julia-set/is-there-anything-novel-left-to-do-in-m-like-escape-time-fractals-in-2d/msg39681/#msg39681 Now it is too late to test it now.
...
Unit vector kind of influences vector movement in complex plane during iterations thus thining mandelbrot or the opposite, inflating it. (with 3D fractals it literary is like ballon with more or less air.)

EDITED:
No, it certainly is very different. However owerall shape is simmilar. Alsou this modification too shrinks or inflates mandelbrot set, kind of like balloon with more or less air. (Simmilary *|z|^m changes the movement of z vector in complex plane, closer or further from the center of rotation) But, the details are different and shape too.
Maybe the name of formula should reflect mathematical process or the founder or maybe an images.
« Last Edit: June 21, 2021, 12:40:16 PM by Alef »
a catalisator / z=z*sinh(z)-c2

#### claude

• Posts: 1938
##### Re: Kalles Fraktaler 2.15
« Reply #241 on: June 22, 2021, 01:06:34 PM »
more errata for kf-2.15.3

some formulas don't work (compile failure) with OpenCL:
- Mandelbrot power 4 and higher with derivatives enabled (workaround: use Hybrid formula designer)
- formulas 52, 53, 69, 70, 71 with or without derivatives

all fixed in the current work in progress for next release

EDIT and some more

- formulas 23, 24, 25, 26 have problems with the derivatives leading to bad appearance of analytic DE (all fixed for next release)

- built-in formulas 4 (power 3), 20, 42-50 have problems with the derivatives leading to bad appearance of analytic DE (workaround: use hybrid formula designer, which is possible for all of these)

next release is not likely before August, due to holidays.  other things I want to add are special-casing complex-analytic formulas in various places (including hybrid designer which should speed up derivatives for analytic DE and newton zooming etc a fair bit).
« Last Edit: June 24, 2021, 05:33:24 PM by claude, Reason: more bugs »

#### claude

• Posts: 1938
##### Re: Kalles Fraktaler 2.15
« Reply #242 on: June 25, 2021, 02:40:41 PM »
There are so many formulas, but clustered into related families such as burning-ship-like. Maybe have the list be organized more into sub-lists?

In my work in progress for the next release, I added an option for hiding from the formula dropdown list the built-in formulas that can be implemented as hybrid formulas. This makes the list just over 1 page of items instead of around 5 pages.  Coupled with the new buttons to convert between built-in and hybrid formulas I think this would be enough of a usability improvement?

#### gerrit

• 3f
• Posts: 2448
##### Re: Kalles Fraktaler 2.15
« Reply #243 on: June 28, 2021, 06:54:39 PM »
What happened to auto-skew? It seems to have disappeared in .15.

#### claude

• Posts: 1938
##### Re: Kalles Fraktaler 2.15
« Reply #244 on: June 28, 2021, 09:09:09 PM »
What happened to auto-skew? It seems to have disappeared in .15.

in 2.15.3 the new Newton zoom dialog has the option for skewing based on minibrots as before. The other auto-skew has moved to the Transformation dialog (ctrl-t)

in 2.15.4 coming later this summer, right click drag to adjust skew is much more sensibly behaved.

#### Microfractal

• Fractal Feline
• Posts: 154
##### Re: Kalles Fraktaler 2.15
« Reply #245 on: July 02, 2021, 10:04:53 PM »
Formula Idea:
abs(z)^2*exp(2/z)+c

like the formula (by gerrit) z^2 exp(2 a / z) + c
but with abs() on the first z (real and imaginary)

#### saka

• Fractal Phenom
• Posts: 48
##### Re: Kalles Fraktaler 2.15
« Reply #246 on: July 12, 2021, 05:34:07 AM »
Thanks for all your hard work!  I have a request:

All the fractals are upside down, because the imaginary (y) coordinate is flipped. You don't notice with Mandelbrots, but for ships, hybrids and others it gets confusing.  It is also annoying when sharing/importing coordinates.

Can, we add a "Flip y coordinate" option to the view menu and enable it by default (this would result in no change).  Then anyone can disable it, to display a true complex plane (positive imaginary up).  Exported images/kfb/exr should use the setting.  (Perhaps save setting in the .kfr also)

Specifically, where you find an issue:

1. Every fractal is upside down. For example, the manual states the Burning Ship is z := (|x| + i |y|)^p + c, but if you calculate this, the result will be upside down.
(Outside KF world, many use z := (|x| + i |y|)^p - c for the burning ship, which is the mirror image of KF).

2. .kfr File format has negative values for upper plane.

3. Location dialog box has negative values for upper plane.

#### claude

• Posts: 1938
##### Re: Kalles Fraktaler 2.15
« Reply #247 on: July 18, 2021, 09:48:54 PM »
Historically (and currently) in KF, the imaginary axis points down; all coordinates and interactions are self-consistent with this interpretation. The Burning Ship with +C and imaginary axis pointing down, looks like a ship, reflected horizontally from the Burning Ship with -C (as used in the original paper, iirc) and imaginary axis pointing up.  Imaginary axis pointing up is admittedly a lot more common in maths exposition than the other way around.

Flipped/upside down images could potentially be fixed (it is a relatively frequently brought up issue), but there might be a lot to check to get it 100% accurate everywhere.  Could maybe be a checkbox "Imaginary axis points up" in the Transformation dialog (I prefer previously non-existing parameters to default to 0).  Would need to happen before the rotation and skew stuff.  Would be in the KFR like the rest of the transformation stuff.

Meanwhile I made the new window and image size dialog much more compact, with drop down menus instead of loads of radio buttons, as suggested by bezo97 in Fractal Chats Discord.

#### claude

• Posts: 1938
##### Re: Kalles Fraktaler 2.15
« Reply #248 on: July 19, 2021, 01:26:48 PM »
About 2-3 hours of head scratching / debugging and I figured out how to implement Imaginary Axis Points Up in KF-next WIP.  The actual code changes are not so large, mainly adds an extra yflip part to the 2x2 matrix polar (de)composition.  The kf-tile.exe utility is also updated.

#### claude

• Posts: 1938
##### Re: Kalles Fraktaler 2.15
« Reply #249 on: July 19, 2021, 02:05:58 PM »
abs(z)^2*exp(2/z)+c
This is a bit tricky to implement due to technical reasons, so I probably won't do it for the next release.  Maybe later.  I put it on the TODO list.

• Fractal Frankfurter
• Posts: 541
##### Re: Kalles Fraktaler 2.15
« Reply #250 on: July 20, 2021, 09:29:03 PM »
...
All the fractals are upside down, because the imaginary (y) coordinate is flipped. You don't notice with Mandelbrots, but for ships, hybrids and others it gets confusing.

it is a problem. In  mu c programs I add visual check ( mark right upper quadrant):
Code: [Select]
// Check Orientation of z-plane image : mark first quadrant of complex plane // it should be in the upper right position// uses global var :  ...int CheckZPlaneOrientation(unsigned char A[] ){   double Zx, Zy; //  Z= Zx+ZY*i;  unsigned i; /* index of 1D array */  unsigned int ix, iy; // pixel coordinate   fprintf(stderr, "compute image CheckOrientation\n");  // for all pixels of image #pragma omp parallel for schedule(dynamic) private(ix,iy, i, Zx, Zy) shared(A, ixMax , iyMax)   for (iy = iyMin; iy <= iyMax; ++iy){    //fprintf (stderr, " %d from %d \r", iy, iyMax); //info     for (ix = ixMin; ix <= ixMax; ++ix){      // from screen to world coordinate       Zy = GiveZy(iy);      Zx = GiveZx(ix);      i = Give_i(ix, iy); /* compute index of 1D array from indices of 2D array */      if (Zx>0 && Zy>0) A[i]=255-A[i];   // check the orientation of Z-plane by marking first quadrant */    }  }        return 0;}
HTH
« Last Edit: July 20, 2021, 09:44:19 PM by Adam Majewski, Reason: descr »

#### claude

• Posts: 1938
##### Re: Kalles Fraktaler 2.15
« Reply #251 on: July 22, 2021, 01:34:27 PM »
kf-2.15.4 released with new features, bugfixes, speed improvements

Too many changes to mention all of them here, highlights include:
- 3 new formulas (Hidden Mandelbrot, Hidden Mandelbrot a la Cos, Polarbrot)
- ignore or convert between built-ins and hybrids in the Formula dialog
- rewritten GUI for window size / image size
- “imaginary axis points up” option in the Transformation dialog
- Transformation right click drag for skew behaves much more sensibly
- many bugfixes in formulas
- many (mostly small) speed improvements

donations to support my work are welcome via https://mathr.co.uk/kf/kf.html#donate

#### shapeweaver

• Fractal Fanatic
• Posts: 23
##### Re: Kalles Fraktaler 2.15
« Reply #252 on: July 23, 2021, 08:10:52 AM »
[Bug] Zoom size setting ignored if animate zoom is set to true (always uses 2x). It works properly if animate zoom is set to false. This bug existed in earlier versions I think.

#### Microfractal

• Fractal Feline
• Posts: 154
##### Re: Kalles Fraktaler 2.15
« Reply #253 on: July 26, 2021, 08:40:35 PM »
One Bug: If I press rotate several times, the rotation resets to 0 instead of remaining at the previous rotation.

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