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#universalalgebra — Public Fediverse posts

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  1. Charlotte Aten @[email protected] ·

    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 codeberg.org/caten/RealAlgebra

    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 (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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    #lualang #lua #cpp #quaternions #octonions #universalalgebra
  2. Charlotte Aten @[email protected] ·

    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: aten.cool/documents/papers/A%2

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

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    #universalalgebra #mandelbrotset #mandelbrot #fractals #research #academia