#mandelbrot — 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

(2/3)

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

(1/3)

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 \(2.5\).

## 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#

No #photography today, more #mathematics

https://adam-gladstone.pixels.com/featured/vibrant-fractal-spirals-adam-gladstone.html

#ayearforart #buyintoart #fineartamerica #fractal #mandelbrotset #mandelbrot #fediart #giftidea

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!
https://www.sgxengine.com/examples/mandelbrot/html5/mandel.htm #sgx #sfx

Here's something for the more mathematically inclined:

https://adam-gladstone.pixels.com/featured/intricate-fractal-design-adam-gladstone.html

#mathematics #math #fractal #mandelbrot #mandelbrotset #ayeareforart #buyintoart #fineartmamerica #wallart #homedecor

ICYMI,. Here's me showing off some #graphics, from my 20 years in #JavaScript #development: #Mandelbrot 2 of 2 - using #WebWorkers to prove that it's not
-always- a benefit https://www.marquisdegeek.com/mandelworkers #sgx #sfx

Here's me showing off some #graphics, from my 20 years in #JavaScript #development: #Mandelbrot 2 of 2 - using #WebWorkers to prove that it's not
-always- a benefit https://www.marquisdegeek.com/mandelworkers #sgx #sfx

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!
https://www.sgxengine.com/examples/mandelbrot/html5/mandel.htm #sgx #sfx

## mandelbrot 08:28

# syntax

* `nice -19 fraqtive &`
* type *julia*
* variant *conjugate*
* parameters *x 0.4 y 0.5*
* exponent *real=3.02*
* zoom *10^-0.35*
* rotation *17.0 deg*
* formula *Z(n+1)=_Z(n)^2+C*
* generation *2D*
* Resolution *Width 2560 Height 1080*
* Anti Aliasing *Medium*
* Multisampling *4x4*
* Calculation time a few 1000 ms

## Julia Mandelbrot

sources:

man fraqtive(1)

man thunar(1)

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

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

## mandelbrot 06:46

# syntax

* `nice -19 fraqtive &`
* type *julia*
* variant *absolute Im.*
* parameters *x 0.5 y 0.53*
* exponent *real=3.12*
* zoom *10^-0.35*
* rotation *53.0 deg*
* formula *Z(n+1)=_Z(n)^2+C*
* generation *2D*
* Resolution *Width 2560 Height 1080*
* Anti Aliasing *Medium*
* Multisampling *4x4*
* Calculation time a few ms

## Julia Mandelbrot

sources:

man fraqtive(1)

man thunar(1)

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

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

I encountered a #Mystery! This apple looked normal / unblemished until after I cut it in half, when these odd markings appeared. As you can see, they are only surface-deep, the inside is not affected. Of course apples get brown spots now and then, but this... looks so intentional? Aliens?!

#everydayMystery #mandelbrot #apple #weird #foodScience #pleaseExplain #isItAliens #agriculture #farming

## mandelbrot 02:17

# syntax

* `fraqtive`
* type *julia*
* parameters *x=0.6 y=0.7*
* variant *real*
* exponent *real=3.30*
* formula *Z(n+1)=_Z(n)^3.3+C*
* zoom *10^-0.35*
* rotation *15.0 deg*
* generation *2D*
* Resolution *Width 2560 Height 1080*
* Anti Aliasing *Medium*
* Multisampling *4x4*

sources:

man fraqtive(1)

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

#mathematics #programming #mandelbrot #fractals #advanced #Lineair #Algebra #complex #numbers #matrix #technology #OpenSource #no #TV

They've made some pretty deep #Mandelbrot zooms by now. 10^4141 in this case: #fractals
https://www.youtube.com/watch?v=Xjy_HSUujaw

Finally blogged about the evolution of my own #Mandelbrot #fractal rendering app, Fractious in its current #Wasm + #WebGPU iteration. I should warn you, there's a suspiciously high number of mentions of #FORTRAN in this article.
https://rowan.fyi/posts/fractious-deep/

mandelbrot 10:06

md formatted

syntax

• nice -19 fraqtive &
• type julia
• variant absolute Im.
• parameters x 0.62 y 0.5
• exponent real=2.91
• formula Z(n+1)=(ReZ(n)+I|Im(Zn)|)2.91+C
• zoom 10-0.35
• rotation 46.0 deg
• generation 2D
• Resolution Width 2560 Height 1080
• Anti Aliasing Medium
• Multisampling 4x4
• Calculation time a few s

Julia Mandelbrot

sources:

man fraqtive(1)

man thunar(1)

Advanced fractal mathematics by Gerold van Dijk

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

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

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

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

https://en.wikipedia.org/wiki/File:Self-Similarity-Zoom.gif

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

@amiga

## mandelbrot 10:06

# syntax

* `nice -19 fraqtive &`
* type *julia*
* variant *absolute Im.*
* parameters *x 0.62 y 0.5*
* exponent *real=2.91*
* formula *Z(n+1)=(ReZ(n)+I|Im(Zn)|)2.91+C*
* zoom *10^-0.35*
* rotation *46.0 deg*
* generation *2D*
* Resolution *Width 2560 Height 1080*
* Anti Aliasing *Medium*
* Multisampling *4x4*
* Calculation time a few s

## Julia Mandelbrot

sources:

`man fraqtive(1)`

`man thunar(1)`

**Advanced fractal mathematics** by *Gerold van Dijk*

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

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

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

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

https://en.wikipedia.org/wiki/File:Self-Similarity-Zoom.gif

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

## mandelbrot 16:29

# syntax

* `nice -19 fraqtive &`
* type *julia*
* variant *conjugate*
* parameters *x 0.4 y 0.5*
* exponent *real=2.91*
* zoom *10^-0.45*
* rotation *10.0 deg*
* formula *Z(n+1)=_Z(n)^2+C*
* generation *2D*
* Resolution *Width 2560 Height 1080*
* Anti Aliasing *Medium*
* Multisampling *4x4*
* Calculation time a few s

## Julia Mandelbrot

sources:

man fraqtive(1)

man thunar(1)

**Advanced fractal mathematics** by *Gerold van Dijk*

* https://uvs.edu.sr/books/advanced_fractal_math_v2.4.txt
* defunct!

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

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

## mandelbrot 04:19

# syntax

* `nice -19 fraqtive &`
* type *mandelbrot*
* variant *absolute Im.*
* parameters *x 0.51 y 0.53*
* exponent *real=3.11*
* zoom *10^-0.45*
* rotation *20.0 deg*
* formula *Z(n+1)=_Z(n)^2+C*
* generation *2D*
* Resolution *Width 2560 Height 1080*
* Anti Aliasing *Medium*
* Multisampling *4x4*
* Calculation time a few ms

## Standard Mandelbrot

sources:

man fraqtive(1)

man thunar(1)

**Advanced fractal mathematics** by *Gerold van Dijk*

* https://uvs.edu.sr/books/advanced_fractal_math_v2.4.txt
* defunct!

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

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

## mandelbrot 23:28

# syntax

* `fraqtive`
* type *mandelbrot*
* parameters *nvt*
* variant *real*
* exponent *real=2.61*
* formula *Z(n+1)=_Z(n)^2+C*
* zoom *10^-0.35*
* rotation *100.0 deg*
* generation *2D*
* Resolution *Width 2560 Height 1080*
* Anti Aliasing *Medium*
* Multisampling *4x4*

sources:

man fraqtive(1)

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

#mathematics #programming #mandelbrot #fractals #advanced #Lineair #Algebra #complex #numbers #matrix #technology #OpenSource

As promised, here's one of my #fractal images:

https://adam-gladstone.pixels.com/featured/intricate-fractal-patterns-adam-gladstone.html

#maths #math #mathematics #ayearforart #buyintoart #fineartamerica #mandelbrot #mandelbrotset #giftidea #mastoart #fedigiftshop

## mandelbrot 12:48

# syntax

* `nice -19 fraqtive &`
* type *mandelbrot*
* variant *normal*
* exponent *real=2.11*
* zoom *10^-0.35*
* rotation *155.0 deg*
* formula *Z(n+1)=_Z(n)^2+C*
* generation *2D*
* Resolution *Width 2560 Height 1080*
* Anti Aliasing *Medium*
* Multisampling *4x4*
* Calculation time 14248ms

## Standard Mandelbrot

sources:

**Advanced fractal mathematics** by *Gerold van Dijk*
* https://uvs.edu.sr/books/advanced_fractal_math_v2.4.txt
* defunct!

man fraqtive(1)

man thunar(1)

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

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

RE: https://wehavecookies.social/@denise/116585016946727331

mandelbrot 12:25

md formatted

syntax

• nice -19 fraqtive &
• type julia
• parameters x=0.33 y=0.8145
• variant Conjugate
• exponent real=1.87
• zoom 10-0.35
• rotation 105.0 deg
• formula Z(n+1)=_Z(n)2+C
• generation 2D
• Resolution Width 2560 Height 1080
• Anti Aliasing Medium
• Multisampling 4x4
• Calculation time 4248ms

Rotated for conveniece on desktop display panels

sources:

moi: patience!

man fraqtive(1)

man thunar(1)

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

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

@denise