Talk:Mandelbrot set

The pseudo code says:

while (x^2 + y^2 ≤ 2^2 AND iteration < max_iteration) do

while the python code says:

if abs(z) >= bound:

I think the first instance should be 'y^2 < 2^2' or the second one 'abs(z) > bound'. — Preceding unsigned comment added by ~2026-13321-88 (talk) 07:51, 1 March 2026 (UTC)

The Mandelbrot set was used as a decorative motif for a kind of space portal in Episode 11 of Space 1999. The episode was broadcast in 1975: https://editorial01.shutterstock.com/wm-preview-1500/813719gk/4fbb5a0c/gtv-archive-shutterstock-editorial-813719gk.jpg

Quite often I find myself in the want of looking at a picture of the set with coordinate grid overlay. However obvious this request may appear, I struggle to find a quality picture like that online, and there seem to be none on Wikimedia. What I mean is an image where one can see clearly where the origin is, where 1 and i are, how far and in which directions on the Complex number plane the set extends. I've made a picture like that for my own use, do you think it would be useful to display on this page? melikamp (talk) 23:29, 23 September 2025 (UTC)

Looks like it's on Wikimedia!

https://commons.wikimedia.org/wiki/Category:Fractals_created_by_User:_Aokoroko

Pascal, ffmpeg and FASM. Image, Video, gif. Great job! Aokoroko (talk) 13:39, 28 September 2025 (UTC)

None of the linked ones have a coordinate grid, though may be I am missing something. melikamp (talk) 06:17, 29 September 2025 (UTC)

Fragment of the Mandelbrot set, coordinates: -0.53574936096559973, 0.52584516139308231 width 0.0000000000000035

This is a coordinate grid!!!

And it in Pascal language. This code can be compiled with Delphi or with Free Pascal. Aokoroko (talk) 17:42, 30 September 2025 (UTC)

I went ahead and added it to the Definition section, hope it's useful :) melikamp (talk) 00:33, 3 October 2025 (UTC)

Is it possible to use the Mandelbrot set - Art and the Mandelbrot set? Is it before References in Popular Culture? Here are mine - https://commons.wikimedia.org/wiki/Category:Fractals_created_by_User:_Aokoroko Many have recognized them as high-quality images! Can I make 10 of them? Aokoroko (talk) 19:24, 30 September 2025 (UTC)

Undid revision (((((((( "A stupendously large number of other pictures have been generated" - WHERE??? Can you find at least one? Where And "Quality image"??? Aokoroko (talk) 09:03, 7 October 2025 (UTC)

https://commons.wikimedia.org/wiki/Commons:Quality_images

Non-photographic media 37.215.35.217 (talk) 10:24, 8 October 2025 (UTC)

I would like to discuss the recent undo of my contribution. While I understand the article already contains many images, I believe the addition of these specific renders is justified by several factors that align with WP:DUE and WP:IMAGEQUALITY:

1. Technical Superiority (Anti-aliasing): Unlike many existing examples, these images were rendered using 8x8 (64 samples per pixel) supersampling. This eliminates moiré patterns and aliasing artifacts, providing a mathematically cleaner representation of the set's boundary compared to standard renders.
2. Visual Depth and Palette: The color palette was algorithmically generated to maximize the dynamic range of the iteration layers. This allows for 24-bit TrueColor gradients that reveal structural details in high-density areas which are often lost in "flat" or low-bit palettes.
3. Community Recognition: These files have been officially vetted and designated as Quality Images on Wikimedia Commons. This status confirms they meet high technical and aesthetic standards, distinguishing them from the "stupendously large number" of low-quality, automated fractal generations.
4. Unique Locations: These renders focus on specific, high-magnification features of the Mandelbrot set that illustrate its self-similarity better than existing overview shots.

I believe replacing or supplementing older, lower-resolution images with these QI-standard renders significantly improves the visual quality of the encyclopedia. I would appreciate the community's feedback on integrating at least the most representative of these works. Fractals by Aokoroko Aokoroko (talk) 14:43, 28 January 2026 (UTC)

Art and the Mandelbrot Set

Some people enjoy finding interesting geometric shapes in the Mandelbrot set. Here are a few examples of beautiful regions in this set:

May I? Aokoroko (talk) 14:49, 1 February 2026 (UTC)

Quality Image Status: It is important to note that these images have been vetted under the Quality Images guidelines on Wikimedia Commons and officially designated as Quality Images. This status confirms they meet high technical and aesthetic standards, distinguishing them from common fractal renders.

Artistic vs. Technical Value: These renders have already been integrated into the 'Art' sections of the main Fractal and Mandelbrot set pages on Wikimedia Commons. This indicates that the broader community recognizes their illustrative value. Aokoroko (talk) 09:30, 2 February 2026 (UTC)

So. There are 256 colors to start with!

pal[a][0]:=round(127+127*cos(2*pi*a/255)); // Green

pal[a][1]:=round(127+127*sin(2*pi*a/255)); // Blue

pal[a][2]:=Random(256); // Red

And the 256 files are an animation—one file per file. When you "rotate" the palette, you only change 1024 bytes (256 entries of 4 bytes), so it works incredibly fast even on older hardware.

An animation of 256 files, where each file is a separate frame, is an image sequence, which is usually assembled into a single animated format. GIF formats are most often used for such purposes. When working with so many files, it's important to number them correctly (e.g., frame_001.bmp, frame_002.bmp...) for automatic import. Here it is:

ffmpeg -i frame_%%03d.bmp "Mandelbrot Set Color Cycling Animation 600px 58.gif"

But then! Then, look! If you look at most programs, you'll see the problem: only 256 colors and obvious "steps" between color transitions (so-called color banding). I don't like this! So I decided—there would be a whole new level of quality! I implemented true supersampling (antialiasing)—with 8x8 antialiasing (64 passes per pixel!!!)

That is, not 1080 by 1080 pixels, but 8x8 more! 8640 by 8640 pixels! Then, these 64 passes are smoothly reduced by one pixel—and no longer 8-bit, but 24-bit TrueColor!

24-bit color (TrueColor) is an image encoding method that uses 8 bits per channel (RGB: red, green, blue), yielding 16,777,216 shades. Unlike 8-bit color (256 colors), TrueColor delivers realistic color reproduction by eliminating visible boundaries between shades and is considered the standard for modern displays and photos.

Key differences and features of 24-bit TrueColor:

Color depth: Each pixel is described by 24 bits (3 bytes), allowing for the expression of over 16 million colors, exceeding the capabilities of the human eye.

Channel separation: 8 bits (256 brightness levels) are allocated to each of the three colors: red, green, and blue.

Advantages: Provides smooth gradients, high color accuracy, and is ideal for photographs and complex images.

So ALL my animations, videos, and images are 24-bit color (TrueColor)!

I have an animation, for example:

https://commons.wikimedia.org/wiki/File:Mandelbrot_Set_Color_Cycling_Animation_600px_58.gif

Or a video, for example:

https://commons.wikimedia.org/wiki/File:Mandelbrot_Set_Color_Cycling_Video_1080p_4.webm

And an image, for example:

https://commons.wikimedia.org/wiki/File:Mandelbrot_Set_Image_76.png

If possible, I'd like to call it "Art and the Mandelbrot Set"... After all, it says, "Some people enjoy finding interesting geometric shapes in the Mandelbrot set. Here are some examples of beautiful regions in the Mandelbrot set." Aokoroko (talk) 14:50, 3 February 2026 (UTC)

Any statement like "Some people enjoy finding interesting geometric shapes in the Mandelbrot set" would require a citation to a reliable source. And no region of the Mandelbrot set can be called "beautiful" in Wikipedia's voice. Stepwise Continuous Dysfunction (talk) 01:48, 4 February 2026 (UTC)

Need a link to a reliable source? This will do: https://commons.wikimedia.org/wiki/Commons:Quality_images/Subject/Non_photographic_media And here's another one: This image has been assessed using the Quality image guidelines and is considered a Quality image.

And https://commons.wikimedia.org/wiki/Mandelbrot_set

And https://commons.wikimedia.org/wiki/Fractal Aokoroko (talk) 09:29, 4 February 2026 (UTC)

Wikimedia Commons, like Wikipedia itself, is user-generated content and not a reliable source in the sense needed here. Stepwise Continuous Dysfunction (talk) 22:20, 4 February 2026 (UTC)

WP:PLOTSOURCE

WP:PRIMARY

Art and the Mandelbrot Set Some people enjoy finding interesting shapes in the Mandelbrot set and assembling them. Below are other examples of beautiful regions of the Mandelbrot set. Many people write their own fractal generator programs to provide maximum flexibility in the image creation process.

If you look at most programs, you'll see the problem: only 256 colors and obvious "steps" between color transitions (so-called color banding). I don't like this! So I decided—there would be a completely different level of quality! I implemented true supersampling (antialiasing)—with 8x8 antialiasing (64 passes per pixel!!!) That is, not 1080 by 1080 pixels, but 8x8 more! 8640 by 8640 pixels! And then these 64 passes reduce the image by one pixel, but smoothly—and no longer 8-bit, but 24-bit TrueColor!

WP:SKY

WP:CITENEED Aokoroko (talk) 10:05, 5 February 2026 (UTC)

So I want Mandelbrot on Wikipedia!

This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.

The person who associated a work with this deed has dedicated the work to the public domain

This image has been assessed using the Quality image guidelines and is considered a Quality image.

That is, not 1080 by 1080 pixels, but 8x8 pixels larger! 8640 by 8640 pixels! And then these 64 passes reduce the resolution by one pixel, but smoothly – and no longer 8-bit, but 24-bit TrueColor – only I have that!

There's no one else in the entire universe!

No group! There's only me!

What are other developers doing? I studied popular projects like https://www.ultrafractal.com/ or https://xaos-project.github.io/ – and nope! They don't have that! Aokoroko (talk) 14:53, 5 February 2026 (UTC)

github:

https://github.com/Divetoxx/Mandelbrot

and English in Habr:

https://habr.com/articles/995936/

Aokoroko (talk) 16:55, 15 February 2026 (UTC)

θ== Proposal: Adding information about high-fidelity rendering (SSAA and 80-bit precision) ==

Hello. I noticed that the current "Image rendering" section could be improved by mentioning modern techniques for noise reduction and deep-zoom precision.

I would like to propose adding information about:

1. 8x8 Supersampling (SSAA): Using 64 samples per pixel with direct RGB-space integration to eliminate aliasing and produce smooth 24-bit TrueColor gradients.
2. 80-bit Extended Precision: The use of long double (x87 FPU) to push the zoom limit to (10,000x deeper than standard 64-bit double).

I have already documented a full C++ implementation of these methods on Rosetta Code https://rosettacode.org/wiki/Mandelbrot_set#High-Fidelity_C++_Implementation_(80-bit,_64x_SSAA,_OpenMP) and uploaded a high-resolution sample to Wikimedia Commons https://commons.wikimedia.org/wiki/File:Mandelbrot_Set_Image_49.png

Would it be appropriate to add a brief mention of these techniques to the article, or perhaps update the visual gallery with a higher-fidelity rendering that demonstrates these advantages? I'm looking for feedback from the community. Aokoroko (talk) 12:45, 18 February 2026 (UTC)

I completely agree that Wikipedia must be based on secondary sources. My proposal is not to introduce "original research," but to document standard computational techniques for fractal rendering that are currently underrepresented in the article.

To address the request for peer-reviewed sources, I refer to:

1. On Supersampling (SSAA) for Fractals: The use of oversampling to mitigate aliasing artifacts in fractal boundaries is a well-established technique described in:
   • Peitgen, H.-O., & Saupe, D. (Eds.). (1988). The Science of Fractal Images. Springer-Verlag. (Chapters 3 & 4 discuss rendering algorithms and antialiasing).
   • Glassner, A. S. (1995). Principles of Digital Image Synthesis. Morgan Kaufmann. (Details on stochastic and grid-based supersampling).
2. On Extended Precision (80-bit/long double): The necessity of extended precision for deep-zoom fractal exploration to avoid rounding errors and "pixelation" is documented in:
   • Milnor, J. (2006). Dynamics in One Complex Variable. Princeton University Press. (Technical discussions on numerical stability in iteration).
   • Higham, N. J. (2002). Accuracy and Stability of Numerical Algorithms. SIAM. (On the impact of hardware-level precision like x87 80-bit floats).

I propose to use my provided Rosetta Code implementation and Wikimedia Commons image merely as illustrative examples of these established scientific principles, ensuring that the technical section of the article reflects current computing standards (OpenMP parallelization and sub-pixel integration).

I would appreciate your guidance on how to integrate these citations into the "Image rendering" section correctly. Aokoroko (talk) 07:37, 19 February 2026 (UTC)

A brief mention of improvements could be mentioned if supported by reliable sources. Anything like an implentation should not be given. Arguably the existing Python implementation should be removed. Sławomir Biały (talk) 08:41, 19 February 2026 (UTC)

Thank you for the feedback, @Sławomir Biały. I agree that Wikipedia is not a code repository. I support the idea of focusing on a brief technical mention of anti-aliasing (SSAA) and extended precision (long double) based on the reliable sources mentioned (Peitgen & Saupe, Glassner).

I understand. My implementation is in C++ with OpenMP and 80-bit precision, which is much more performant than Python for fractal rendering. However, I agree that source code may be redundant in the main article.

If we move the code implementation to Rosetta Code (where it can be properly documented), could we update the 'Image rendering' section with a brief mention of these techniques (SSAA and extended precision) and use the 64x SSAA image to illustrate the result? This would provide encyclopedic value without the clutter of source code. Aokoroko (talk) 12:26, 19 February 2026 (UTC)