#fractals — Public Fediverse posts

And that's not all! I have written a custom Lua map generator for #Luanti which allows you to explore these fractals in real time. You can find this at https://codeberg.org/caten/rpsland and hopefully on the Luanti ContentDB soon.

This mod works with #Mineclonia and Minetest Game and uses the shape of a given 3D algebra's analogue of the Mandelbrot set in order to draw terrain. Fractal noise is used to introduce some more variety and several options are available to tweak and twist these fractals to your liking. I've already spent a ton of time hanging out, exploring, and just generally enjoying these worlds. I hope you have as much fun trying this thing out as I had making it.

#math #mathematics #fractals #Mandelbrot #MandelbrotSet #Lua #MinetestGame

But wait, there's more! I also wrote a C++ program and Lua scripts to help you make animations of these higher-dimensional fractals. You can find these at https://codeberg.org/caten/RealAlgebraPlot

Not only can you see animations of the rock-paper-scissors fractal of central interest in my paper, you can also take slices of even higher-dimensional fractals coming from other real algebras, such as the octonions.

I wrote everything here from scratch as much as possible, so it has basically zero dependencies. I even opted to use Netpbm (https://en.wikipedia.org/wiki/Netpbm) so that I'd have an easy time writing image files directly without using a library. I am using #GraphicsMagick to produce animations. The same utility can be used to convert the output image files to a more familiar format like png.

#math #mathematics #algebra #analysis #ComplexAnalysis #fractals #Mandelbrot #MandelbrotSet #UniversalAlgebra #octonions #quaternions #cpp #Lua #LuaLang

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I'm extremely pleased to announce my newest paper is now available! In «A rock-paper-scissors Mandelbrot set» I study the analogue of the classic Mandelbrot set fractal over the 3-dimensional rock-paper-scissors algebra. This paper details a generalization of the methods of complex dynamics to arbitrary finite-dimensional real algebras. I found some surprising connections between the study of holomorphy in these algebras and their basic algebraic properties, as well as between the classic Mandelbrot set and its higher-dimensional cousins. This is my first foray into hypercomplex analysis, so it might come as a surprise if you've been following me, but over the past several months I thought it would do me some good to go back to my roots, zoom into some fractals, and play rock-paper-scissors. Here's the paper: https://aten.cool/documents/papers/A%20rock-paper-scissors%20Mandelbrot%20set%20[2026].pdf

#math #mathematics #algebra #analysis #ComplexAnalysis #academia #research #fractals #Mandelbrot #MandelbrotSet #UniversalAlgebra

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@FotoVorschlag 'Genoppt (oberflächenstruktur)' #FotoVorschlag

Zwei Bilder aus dem Archiv, Romanesco Brokkoli, damals bisschen mit dem Makro gespielt.

Interessanter Artikel dazu: https://www.sciencetimes.com/articles/29586/20210210/math-behind-beauty-romanesco-broccoli-explained.htm

#Fractals #BW #macrophotography #abstract #nature

Sunday is fun day: back to my #Fractals for #Playdate project. Sierpiński Triangle is a good pick. :)

#swift #EmbeddedSwift

#MissKitty talks about #fractals because there are patterns of recurrence that give clues. Miss Kitty talks about #recursion because what is the answer to which part of #infinity is not infinite? And there being no case where that is true, #miracles are an #imagination away++. #Mind #Technology 🔦🔦🔦

🎭 When 𝘗𝘩𝘺𝘴𝘪𝘤𝘴 meets #Art, quantum magic happens! ✨ Explore the #universe where #thermodynamics shapes aesthetics and #entropy crafts beauty. From #fractals to cosmic symmetry, #science is the ultimate creator. 🌌 Discover the #Wissenschaft behind the masterpieces! 🎨⚛️ #PhysicsArt #Stem #SciArt

Designing an L-system language and interpreter

#Coding #Programming #Tech #Fractal #Fractals #Language #Languages #Declarative #Math #Maths #Mathematics #Mathematical #System #Systems #Compiler #Interpreter #C #CProgramming #C_Programming #Programming_Language

## mandelbrot 06:48

# syntax

* `nice -19 fraqtive &`
* type *julia*
* variant *amsolute IM*
* parameters *x 0.2 y 0.7*
* exponent *real=3.01*
* zoom *10^-0.25*
* rotation *60.0 deg*
* formula *Z(n+1)=(Re(Z(n))+i|Im(Zn)|)^3.01+C*
* control G
* generation *2D*
* Resolution *Width 2560 Height 1080*
* Anti Aliasing *Medium*
* Multisampling *4x4*
* Calculation time a whopping 42000 ms

## Julia Mandelbrot

sources:

man fraqtive(1)

man ls(1)

man thunar(1)

https://en.wikipedia.org/wiki/Mandelbrot_set

https://en.wikipedia.org/wiki/Mathematics

#mathematics #math #CPU #coprocessor #programming #mandelbrot #julia #fractals #advanced #Lineair #Algebra #complex #numbers #formulas #matrix #technology #OpenSource #no #TV#