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#mandelbrot — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #mandelbrot, aggregated by home.social.

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  1. 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 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

  2. 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 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

  3. 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 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

  4. 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 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

  5. 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 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

  6. 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

    (2/3)

  7. 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

    (2/3)

  8. 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

    (2/3)

  9. 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

    (2/3)

  10. 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

    (2/3)

  11. 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

    (1/3)

  12. 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

    (1/3)

  13. 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

    (1/3)

  14. 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

    (1/3)

  15. 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

    (1/3)

  16. When I was an engineering undergrad in the early 1980s, #chaos theory and #fractal geometry were coming into vogue, thanks to #Mandelbrot's excellent book "The Fractal Geometry of Nature". What struck me about, then and now, about chaos processes is their description of how a simple, predictable, ordered process, under certain conditions, suddenly explodes into a wild, chaotic results.

    Of relevance to the present quagmire of our #IT industry is the Verhulst population growth function: \(x_{t+1} = (1 + r)^t x_t\), where \(t\) is time and \(r\) is growth rate. The dynamic process emerges, when this function is iterated over time.

    When \(r < 2.0\), the population dynamic eventually converges to a stable number. When \(r = 2.3\), the population oscillates between high and low numbers. When \(r ≥ 2.5\), the population dynamic transitions into a chaotic process.

    I wonder if the present growth rate \(r\) of the IT industry has risen way above \(2.5\).

  17. When I was an engineering undergrad in the early 1980s, #chaos theory and #fractal geometry were coming into vogue, thanks to #Mandelbrot's excellent book "The Fractal Geometry of Nature". What struck me about, then and now, about chaos processes is their description of how a simple, predictable, ordered process, under certain conditions, suddenly explodes into a wild, chaotic results.

    Of relevance to the present quagmire of our #IT industry is the Verhulst population growth function: \(x_{t+1} = (1 + r)^t x_t\), where \(t\) is time and \(r\) is growth rate. The dynamic process emerges, when this function is iterated over time.

    When \(r < 2.0\), the population dynamic eventually converges to a stable number. When \(r = 2.3\), the population oscillates between high and low numbers. When \(r ≥ 2.5\), the population dynamic transitions into a chaotic process.

    I wonder if the present growth rate \(r\) of the IT industry has risen way above \(2.5\).

  18. When I was an engineering undergrad in the early 1980s, #chaos theory and #fractal geometry were coming into vogue, thanks to #Mandelbrot's excellent book "The Fractal Geometry of Nature". What struck me about, then and now, about chaos processes is their description of how a simple, predictable, ordered process, under certain conditions, suddenly explodes into a wild, chaotic results.

    Of relevance to the present quagmire of our #IT industry is the Verhulst population growth function: \(x_{t+1} = (1 + r)^t x_t\), where \(t\) is time and \(r\) is growth rate. The dynamic process emerges, when this function is iterated over time.

    When \(r < 2.0\), the population dynamic eventually converges to a stable number. When \(r = 2.3\), the population oscillates between high and low numbers. When \(r ≥ 2.5\), the population dynamic transitions into a chaotic process.

    I wonder if the present growth rate \(r\) of the IT industry has risen way above \(2.5\).

  19. When I was an engineering undergrad in the early 1980s, #chaos theory and #fractal geometry were coming into vogue, thanks to #Mandelbrot's excellent book "The Fractal Geometry of Nature". What struck me about, then and now, about chaos processes is their description of how a simple, predictable, ordered process, under certain conditions, suddenly explodes into a wild, chaotic results.

    Of relevance to the present quagmire of our #IT industry is the Verhulst population growth function: \(x_{t+1} = (1 + r)^t x_t\), where \(t\) is time and \(r\) is growth rate. The dynamic process emerges, when this function is iterated over time.

    When \(r < 2.0\), the population dynamic eventually converges to a stable number. When \(r = 2.3\), the population oscillates between high and low numbers. When \(r ≥ 2.5\), the population dynamic transitions into a chaotic process.

    I wonder if the present growth rate \(r\) of the IT industry has risen way above \(2.5\).

  20. When I was an engineering undergrad in the early 1980s, #chaos theory and #fractal geometry were coming into vogue, thanks to #Mandelbrot's excellent book "The Fractal Geometry of Nature". What struck me about, then and now, about chaos processes is their description of how a simple, predictable, ordered process, under certain conditions, suddenly explodes into a wild, chaotic results.

    Of relevance to the present quagmire of our #IT industry is the Verhulst population growth function: \(x_{t+1} = (1 + r)^t x_t\), where \(t\) is time and \(r\) is growth rate. The dynamic process emerges, when this function is iterated over time.

    When \(r < 2.0\), the population dynamic eventually converges to a stable number. When \(r = 2.3\), the population oscillates between high and low numbers. When \(r ≥ 2.5\), the population dynamic transitions into a chaotic process.

    I wonder if the present growth rate \(r\) of the IT industry has risen way above \(2.5\).

  21. ## 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)

    en.wikipedia.org/wiki/Mandelbr

    en.wikipedia.org/wiki/Mathemat

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

  22. ## 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)

    en.wikipedia.org/wiki/Mandelbr

    en.wikipedia.org/wiki/Mathemat

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

  23. ## 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)

    en.wikipedia.org/wiki/Mandelbr

    en.wikipedia.org/wiki/Mathemat

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

  24. ## 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)

    en.wikipedia.org/wiki/Mandelbr

    en.wikipedia.org/wiki/Mathemat

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

  25. ## 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)

    en.wikipedia.org/wiki/Mandelbr

    en.wikipedia.org/wiki/Mathemat

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

  26. ICYMI Here's me showing off some #graphics, from my 20 years in #JavaScript #development: #Mandelbrot 1 of 2 - obsfuscated and optimised to zoom in
    real-time, even back in the day!
    sgxengine.com/examples/mandelb #sgx #sfx

  27. ICYMI Here's me showing off some #graphics, from my 20 years in #JavaScript #development: #Mandelbrot 1 of 2 - obsfuscated and optimised to zoom in
    real-time, even back in the day!
    sgxengine.com/examples/mandelb #sgx #sfx