gamma correction and location of zoom image

  • 11 Replies
  • 236 Views

0 Members and 1 Guest are viewing this topic.

Offline Adam Majewski

  • *
  • Fractal Feline
  • **
  • Posts: 194
« on: November 10, 2019, 09:32:51 AM »
Hi
this is zoom in the standard Mandelbrot set ( z^2+c)
Can you find it's location ?
Original image : https://www.math.univ-toulouse.fr/~cheritat/wiki-draw/index.php/Mandelbrot_set
It is related with gamma correction
See also : https://gitlab.com/adammajewski/mandelbrot_wiki_ACh

TIA



Linkback: https://fractalforums.org/programming/11/gamma-correction-and-location-of-zoom-image/3186/

Offline kohlenstoff

  • *
  • Strange Attractor
  • ******
  • Posts: 81
« Reply #1 on: November 12, 2019, 06:27:57 PM »
This is a modified mandelbrot. Maybe distorted by the used software. Look at the minibrots. If this would be the standard Mandelbrot, they would be symmetrical and identical to the large one.

Offline Adam Majewski

  • *
  • Fractal Feline
  • **
  • Posts: 194
« Reply #2 on: November 12, 2019, 06:38:29 PM »
Thx for the answer, but :

http://www.fractalforums.com/mandelbrot-and-julia-set/how-distorted-can-a-minibrot-be/

so IMHO there are distorted mini Mandelbrot sets in classic Mandelbrot set

Offline claude

  • *
  • 3f
  • ******
  • Posts: 1272
    • mathr.co.uk
« Reply #3 on: November 13, 2019, 02:08:42 AM »
This is my reasoning so far:

The outer light filaments have 3-way spirals.  So the first angle is {1,2}/3.
The inner light filaments have 18-way spirals.  So the next angle is {1,5,7,11,13,17}/18.
There are dark embedded Julia sets visible in the light filaments, so the zoom must have passed an island near its seahorse valley (because of the shape of the EJSs).
There is no additional shape stacking, so the zoom passed at most one island.
The thick filaments are tuned by an island.
The outer thick filaments have 2-way spirals.  So the first angle from the island is 1/2.
The inner thick filaments have 11-way spirals.  So the second angle from the island is {1..10}/11.
The largest visible island is highly distorted, which occurs at the lowest period island in the widest spoke attached to the principal hub.
So the angled internal address of this distorted island detuned relative to its parent is 1 1/2 2 a/11 22 1/2 24.
And the angled internal address of the parent island begins 1 b/3 3 c/18 54 1/2 ....

Attached is not quite right, probably incorrect choice of numerators and the missing ... in the parent address

Location for MuET for FragM:
Code: [Select]
Zoom = 123456789 Logarithmic
Center = -0.05794121488070425808200419,0.8132682994364264091896378

Offline 3DickUlus

  • *
  • 3f
  • ******
  • Posts: 1399
    • Digilantism
« Reply #4 on: November 13, 2019, 04:51:42 AM »
 :worship:
Fragmentarium is not a toy, it is a very versatile tool that can be used to make toys ;)

https://en.wikibooks.org/wiki/Fractals/fragmentarium

Offline Adam Majewski

  • *
  • Fractal Feline
  • **
  • Posts: 194
« Reply #5 on: November 13, 2019, 04:11:17 PM »

Offline Adam Majewski

  • *
  • Fractal Feline
  • **
  • Posts: 194
« Reply #6 on: November 13, 2019, 04:31:59 PM »
This is my reasoning so far:
...
Location for MuET for FragM:
Code: [Select]
Zoom = 123456789 Logarithmic
Center = -0.05794121488070425808200419,0.8132682994364264091896378
I have copied : https://fractalforums.org/code-snippets-fragments/74/muet/2986
Opened it in the Fragmentarium 2.0. There is no log zoom option here . I have to update Fragmentarium

What means  : Zoom = 123456789 Logarithmic ?
How cen I convert it to the radius ?



Offline claude

  • *
  • 3f
  • ******
  • Posts: 1272
    • mathr.co.uk
« Reply #7 on: November 13, 2019, 05:27:46 PM »
Zoom = 1/ radius
Needs double precision, can't remember if my published muet.frag supports that.

Should work in other Mandelbrot viewers too, but muet has the right gamma correct colouring for this effect. I set Exposure to 2.5.

Offline Adam Majewski

  • *
  • Fractal Feline
  • **
  • Posts: 194
« Reply #8 on: November 13, 2019, 05:53:34 PM »
Zoom = 1/ radius
Needs double precision, can't remember if my published muet.frag supports that.

Should work in other Mandelbrot viewers too, but muet has the right gamma correct colouring for this effect. I set Exposure to 2.5.

In the m-perturbator-gtk

size 1214 803
view 53 -0.05794121488070425808200419e+00 0.8132682994364264091896378e+00  8.100000073710000e-09



real=-5.7941214880704257e-02
imag=8.1326829943642642e-01
radius=8.1000000737099996e-09
precision=105


I can check that period of satellites cardioid is 1368
Increasing iterations dos not improve image



Offline claude

  • *
  • 3f
  • ******
  • Posts: 1272
    • mathr.co.uk
« Reply #9 on: November 13, 2019, 08:10:43 PM »
Quote
Increasing iterations dos not improve image

image is fine, just colouring is not so nice - m-perturbator-gtk is optimized for annotations so contrast is low. I should add an exposure control to adjust filament thickness but that needs supersampling to look good.

Offline Adam Majewski

  • *
  • Fractal Feline
  • **
  • Posts: 194
« Reply #10 on: November 17, 2019, 09:17:08 AM »
precision is 100
does it mean that using standard precision ( long double) I can not make a good image ?

https://en.wikibooks.org/wiki/Fractals/Computer_graphic_techniques/2D/plane#Precision

Offline claude

  • *
  • 3f
  • ******
  • Posts: 1272
    • mathr.co.uk
« Reply #11 on: November 17, 2019, 12:29:23 PM »
m-perturbator-gtk uses more precision for the reference to make zooming in smoother (it can reuse calculations)

The precision needed for plain rendering without perturbation depends on pixel spacing which can be calculated from radius and image dimensions. Radius of this image should be fine with double for screen sized images.


xx
Camera location

Started by molkko on Mandelbulber

2 Replies
260 Views
Last post January 10, 2018, 05:58:46 PM
by molkko
xx
If a fractal location is never rendered - does it exist?

Started by Fraktalist on Fractal Philosophy

9 Replies
615 Views
Last post August 02, 2019, 06:50:13 AM
by hobold
xx
Zoom on GPU

Started by mrmath on Fractal movie gallery

0 Replies
217 Views
Last post December 31, 2017, 08:11:43 PM
by mrmath
xx
How do I zoom in 'just a little bit'?

Started by fractal on Kalles Fraktaler

3 Replies
73 Views
Last post August 17, 2019, 10:51:26 PM
by gerrit
xx
M-set zoom

Started by gerrit on Fractal movie gallery

85 Replies
5090 Views
Last post December 02, 2018, 06:46:37 AM
by gerrit