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Author Topic: Lake  (Read 829 times)
Description: Herman Ring c-plane M-Set image
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Fractal Senior
Posts: 2592

« on: January 30, 2009, 02:35:31 AM »

This image results from zooming into the Herman Ring Mandelbrot c-plane, with a = 0.21803398. With this parameter value, there is a large minibrot left of the origin on the x-axis, facing right, with curls of matter funneling into its cusp. Those curls contain spiral structures centered on lakes like the one in this image. The lake, and each of its miniature clones, is a region where points converge to zero instead of escape.

(Note: this description of where to zoom depends on the choice of critical point. If the described structures aren't left of the origin, look for them right of the origin with everything reversed left for right, or use the other critical point.)

Two gradient layers are used -- one with blues for the lake, and a yellow-brown-dark green-light green-yellow-burnt orange one for the shore. (Technically, the first colors points converging to 0 and the second diverging points.)

Overlaying them is a 75%-transparent multiplicative distance estimator layer, with:
* white further than one pixel from the M-Set
* Shading logarithmically to black 1/10,000 of a pixel from the M-set
* black within 1/10,000 of a pixel of the M-Set.
This layer emphasizes the contours of the basin boundaries and M-set.

Minibrots can be seen dotting the shore; these are solid black and contain points that converge to finite attractors other than 0.

Freely redistributable and usable subject to the Creative Commons Attribution license, version 3.0.

This one gave me trouble. I could not get my jpeg encoder to do justice to this image -- the beautiful blue lake in the middle always came out distinctly banded, even with 4:4:4 encoding. So I got someone to host the original png (atpic only accepts jpegs). Right click and save as, or just click, to see it in its full 2048x1536 glory. And don't hammer the server it's on. There's a 5 gig monthly bandwidth limit there, and my friend is hosting some other stuff there and will probably delete lake.png if it starts to draw too much traffic.

If anyone knows of a gimmick, special program, or other way to get a decent jpg version of this image (no banding! at least, more noticeable than the subtle banding you can find if you peer very closely at the png), I'm all ears.

Detailed stats:

Name: Lake
Date: January 29, 2009
Fractal: Herman Ring Mandelbrot, c-plane
Location: angle parameter = 0.21803398, zoomed mildly near cusp of large axis minibrot left of origin
Depth: Shallow
Min Iterations: 1
Max Iterations: 26041
Layers: 3
Anti-aliasing: 3x3, threshold 0.10, depth 1
Preparation time: 10 minutes
Calculation time: 30 minutes (2GHz dual-core Athlon XP)

« Last Edit: January 30, 2009, 03:36:15 AM by Pauldelbrot, Reason: fix aspect ratio » Logged

Posts: 157

« Reply #1 on: January 30, 2009, 03:09:35 AM »

Nice image. Thanks for the detailed information on it.

Regarding the banding -- I've not been able to manage this problem either. It becomes much worse in compressed animations, even at quite high bit rates with a good MP4 encoder.

Zoom deeply.
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