• January 18, 2021, 08:19:35 PM

Login with username, password and session length

Author Topic:  Reverse engineering a fractal image?  (Read 466 times)

0 Members and 1 Guest are viewing this topic.

Offline marcm200

  • 3c
  • ***
  • Posts: 893
Reverse engineering a fractal image?
« on: February 06, 2019, 11:48:02 AM »
I was wondering whether one could retrieve formula information from a calculated image of, say, a black and white Julia set. Since it only has a finite number of points with finite precision, there's hardly much information present except for the shape.

Is this information sufficient to deduce one c value (might not be the single one existing) that would deliver said Julia set when computed? Or is escape iteration information necessary?

And what about other types of fractals?

Does anyone know of literature/articles dealing with that topic? Or has experience in doing so?

Linkback: https://fractalforums.org/fractal-mathematics-and-new-theories/28/reverse-engineering-a-fractal-image/2598/


Offline marcm200

  • 3c
  • ***
  • Posts: 893
Re: Reverse engineering a fractal image?
« Reply #2 on: February 07, 2019, 10:13:47 AM »
Thanks a lot! Seems one needs a lot of general information about the overall structure of the Mandelbrot set, just the image and the general iteration formula doesn't seem enough.

Would be interesting to see how the Julia sets behave with finite resolution and how many different shapes there are. I might take a closer look into that.

Offline claude

  • 3f
  • ******
  • Posts: 1735
    • mathr.co.uk
Re: Reverse engineering a fractal image?
« Reply #3 on: February 07, 2019, 06:11:53 PM »
Julia sets are invariant under both forward and backward iteration.  So perhaps you could phrase it as an optimization problem.  Assuming you don't know the coordinates of the image, but that it is just uniformly scaled and rotated and translated, that requires solving for 3 complex variables a b c:

\[ I = \frac{f_c(a I + b) - b}{a} \] where I is the image of the Julia set

As you have more than 3 pixels (I hope), the system is overconstrained so least squares optimization might work.  For other transformations (eg perspective, for a photo of a poster of a Julia set), the process is similar but there may be more variables.

Maybe the cost function to optimize could be based on distance fields (per pixel distance to Julia set, scaled by derivative of f_c transform at each pixel), such that perfect alignment would minimize the cost?  Not sure exactly how it would work, but maybe it's possible.

Offline marcm200

  • 3c
  • ***
  • Posts: 893
Re: Reverse engineering a fractal image?
« Reply #4 on: February 07, 2019, 07:52:16 PM »
Thanks for the in-depth answer! Now I know where to start.


lamp
Reverse calculation for zoom out => zoom in

Started by FK68 on Kalles Fraktaler

4 Replies
192 Views
Last post September 27, 2020, 12:07:26 AM
by unassigned
clip
how to interpret this fractal image?

Started by v on Noob's Corner

1 Replies
298 Views
Last post January 03, 2020, 09:42:35 AM
by claude
xx
Spurious fractal image

Started by xenodreambuie on Share a fractal

1 Replies
181 Views
Last post December 08, 2020, 10:38:04 AM
by Caleidoscope
xx
Fractal image of the month - Discussion thread

Started by Fractalforums Team on Fractal Image of the Month

174 Replies
7919 Views
Last post January 06, 2021, 10:26:41 PM
by Caleidoscope
xx
Fractal Image of the month - Feb. 2019 And the winners are...?

Started by Caleidoscope on Fractal Image of the Month

14 Replies
1336 Views
Last post February 28, 2019, 02:26:46 PM
by gerson