#mathematicalart — Public Fediverse posts

Circles breathe into circles, a mandala of pure mathematics where every curve is both beginning and end, whispering the universe's oldest secret — that all things return to themselves. In this sacred geometry, infinity wears the humble face of repetition, each ring a world nested within worlds.

#SacredGeometry #CirclesWithinCircles #MathematicalArt #InfinitePatterns #GeometricMandala

https://silverlenz.carrd.co
Zap ⚡ if it resonates — support the transmissions directly:...

A cosmic serpent of nested circles breathes the ancient rhythm of the golden ratio, while a staircase of cyan squares marches diagonally across the universe like digits of an infinite equation. Here, geometry becomes myth — Fibonacci's ghost spiraling through numbered horizons of 23.6, 38.2, and 61.8, where mathematics and eternity share the same heartbeat.

#GoldenRatio #SacredGeometry #FibonacciSpiral #MathematicalArt #InfinitePattern

https://silverlenz.carrd.co
Zap ⚡ if it resonates —...

Circles within circles conspire in sacred geometry, whispering the universe's oldest secret — that every boundary is also a beginning. This mandala of pure line and ratio breathes like a living cosmos, where mathematics becomes meditation.

#SacredGeometry #CirclesOfInfinity #GeometricMandala #MathematicalArt #UnityInPattern

https://silverlenz.carrd.co
Zap ⚡ if it resonates — support the transmissions directly: https://silverlenz.github.io/zack-zaps/

Circles breathe into circles, each curve a whispered secret passed between spheres dancing in sacred, mathematical devotion. A mandala born from pure geometry, where infinity folds upon itself in an endless, elegant embrace.

#SacredGeometry #CircularHarmony #GeometricMandala #InfinitePatterns #MathematicalArt

https://silverlenz.carrd.co
Zap ⚡ if it resonates — support the transmissions directly: https://silverlenz.github.io/zack-zaps/

Julia Doubly Mapped

A while ago I made a fractal that consisted of basically generating a Julia set and using Fractal Trace to map it to the Mandelbrot set. In this one I took the same image and mapped it again, so there's more complexity to the shapes and colors.

#Fractal #Fractals #FractalArt #FridayFractals #Abstract #AbstractArt #Math #Maths #Mathematical #MathArt #MathsArt #MathematicalArt #Geometric #GeometricArt #GIMP #Complexity #DigitalArt #Art #Artwork #MastoArt #ArtistOnMastodon

Julia Doubly Mapped

A while ago I made a fractal that consisted of basically generating a Julia set and using Fractal Trace to map it to the Mandelbrot set. In this one I took the same image and mapped it again, so there's more complexity to the shapes and colors.

#Fractal #Fractals #FractalArt #FridayFractals #Abstract #AbstractArt #Math #Maths #Mathematical #MathArt #MathsArt #MathematicalArt #Geometric #GeometricArt #GIMP #Complexity #DigitalArt #Art #Artwork #MastoArt #ArtistOnMastodon

Polar Fractal

Made by mapping an image to polar coordinates several times, meaning this image is the composition of about 20 or so rectangular-to-polar coordinate mappings. It has resulted in a very complex design.

#Fractal #Fractals #FractalArt #Geometry #Geometric #GeometricArt #GIMP #Math #Maths #Mathematics #Mathematical #MathArt #MathsArt #MathematicalArt #Abstract #AbstractArt #Colorful #Colourful #Experimental #AvantGarde #Digital #DigitalArt #Art #Artwork #MastoArt #ArtistOnMastodon

Polar Fractal

Made by mapping an image to polar coordinates several times, meaning this image is the composition of about 20 or so rectangular-to-polar coordinate mappings. It has resulted in a very complex design.

#Fractal #Fractals #FractalArt #Geometry #Geometric #GeometricArt #GIMP #Math #Maths #Mathematics #Mathematical #MathArt #MathsArt #MathematicalArt #Abstract #AbstractArt #Colorful #Colourful #Experimental #AvantGarde #Digital #DigitalArt #Art #Artwork #MastoArt #ArtistOnMastodon

@gwenbeads the book arrived in the mail today. Unbelievable. This will be a delight to read and delve into. What a unique experience. Thank you so much. #mathematicalart

@gwenbeads the book arrived in the mail today. Unbelievable. This will be a delight to read and delve into. What a unique experience. Thank you so much. #mathematicalart

Hello to the Fediverse :)

https://elkement.art/2025/11/13/hello-to-the-fediverse/

Rainbowcore Lichen

Another Mandelbrot fractal that I made in GIMP.

#Fractal #Fractals #FractalArt #Mandelbrot #MandelbrotSet #Geometry #Geometric #GeometricArt #Rainbow #Rainbowcore #Colorful #Colourful #Psychedelia #Psychedelic #Trippy #GIMP #Math #Maths #MathArt #Mathematics #Mathematical #MathematicalArt #Abstract #AbstractArt #Digital #DigitalAbstract #DigitalArt #Art #Artwork #MastoArt #ArtistOnMastodon

Rainbowcore Lichen

Another Mandelbrot fractal that I made in GIMP.

#Fractal #Fractals #FractalArt #Mandelbrot #MandelbrotSet #Geometry #Geometric #GeometricArt #Rainbow #Rainbowcore #Colorful #Colourful #Psychedelia #Psychedelic #Trippy #GIMP #Math #Maths #MathArt #Mathematics #Mathematical #MathematicalArt #Abstract #AbstractArt #Digital #DigitalAbstract #DigitalArt #Art #Artwork #MastoArt #ArtistOnMastodon

Gilded Treasure

Image made using multiple levels of polar coordinate mappings.

#Geometric #GeometricArt #Math #Maths #Mathematical #MathArt #MathsArt #MathematicalArt #Abstract #AbstractArt #Digital #DigitalArt #Pixel #PixelArt #GIMP #Art #Artwork #MastoArt #ArtistOnMastodon

Alien

Artwork I made by creating an abstract pixel art composition as a base image and then mapping it to polar coordinates.

#Geometric #GeometricArt #MathArt #MathsArt #MathematicalArt #ASCII #ANSI #ASCIIArt #ANSIArt #Space #Spaceship #Alien #Aliens #UFO #Abstract #AbstractArt #Surreal #Surrealist #Surrealism #SciFi #SciFiArt #ScienceFiction #Fantasy #FantasyArt #SpaceArt #Pixel #Pixels #PixelArt #Digital #DigitalArt #GIMP #Trippy #Psychedelic #PsychedelicArt #Art #MastoArt #ArtistOnMastodon

Synthesis

#Computer #ComputerArt #Digital #DigitalArt #Abstract #AbstractArt #Fractal #Fractals #FractalArt #Mandala #Mandalas #Gradient #Rainbow #Rainbowcore #Dreamcore #Scenecore #Math #Maths #Mathematical #MathArt #MathsArt #MathematicalArt #Geometry #Geometric #GeometricArt #GIMP #Color #Colors #Colorful #Colour #Colours #Colourful #Psychedelia #Psychedelic #PsychedelicArt #Retro #RetroAesthetic #RetroFuturism #DOS #MSDOS #ASCII #ANSI #Cyberpunk #CyberpunkArt #Symmetric #Art #MastoArt

Synthesis

#Computer #ComputerArt #Digital #DigitalArt #Abstract #AbstractArt #Fractal #Fractals #FractalArt #Mandala #Mandalas #Gradient #Rainbow #Rainbowcore #Dreamcore #Scenecore #Math #Maths #Mathematical #MathArt #MathsArt #MathematicalArt #Geometry #Geometric #GeometricArt #GIMP #Color #Colors #Colorful #Colour #Colours #Colourful #Psychedelia #Psychedelic #PsychedelicArt #Retro #RetroAesthetic #RetroFuturism #DOS #MSDOS #ASCII #ANSI #Cyberpunk #CyberpunkArt #Symmetric #Art #MastoArt

Lichen

#Fractal #Fractals #FractalArt #Geometry #Geometric #GeometricArt #Abstract #AbstractArt #Digital #DigitalArt #Mandelbrot #MandelbrotSet #Math #Maths #Mathematics #Mathematical #MathArt #MathsArt #MathematicalArt #Complex #Complexity #Green #GIMP #Art #Artwork #FediArt #MastoArt #ArtistOnMastodon

Patterned Quadtree

Manipulation of the quadtree fractal made in GIMP. Original fractal made with Processing.

#Fractal #Fractals #FractalArt #Geometry #Geometric #GeometricArt #Math #Maths #MathArt #Mathematical #MathematicalArt #Abstract #AbstractArt #Digital #DigitalArt #GIMP #Photomanipulation #Square #Squares #Pattern #Patterns #Complex #Complexity #Art #Artwork #MastoArt #ArtistOnMastodon

Patterned Quadtree

Manipulation of the quadtree fractal made in GIMP. Original fractal made with Processing.

#Fractal #Fractals #FractalArt #Geometry #Geometric #GeometricArt #Math #Maths #MathArt #Mathematical #MathematicalArt #Abstract #AbstractArt #Digital #DigitalArt #GIMP #Photomanipulation #Square #Squares #Pattern #Patterns #Complex #Complexity #Art #Artwork #MastoArt #ArtistOnMastodon

Julia Mapped to Mandelbrot

I used the GIMP Fractal Explorer to generate a Julia set, then mapped it to a Mandelbrot set with Fractal Trace. I also played with the colors to make it pretty.

#Fractal #Fractals #FractalArt #Geometry #Geometric #GeometricArt #Math #Maths #Mathematical #MathArt #MathematicalArt #Psychedelic #PsychedelicArt #Abstract #AbstractArt #Generative #GenerativeArt #DigitalArt #GIMP #Art #Artwork #MastoArt #ArtistOnMastodon

Julia Mapped to Mandelbrot

I used the GIMP Fractal Explorer to generate a Julia set, then mapped it to a Mandelbrot set with Fractal Trace. I also played with the colors to make it pretty.

#Fractal #Fractals #FractalArt #Geometry #Geometric #GeometricArt #Math #Maths #Mathematical #MathArt #MathematicalArt #Psychedelic #PsychedelicArt #Abstract #AbstractArt #Generative #GenerativeArt #DigitalArt #GIMP #Art #Artwork #MastoArt #ArtistOnMastodon

Composition

Made by stacking multiple levels of composition of the rectangular-to-polar coordinate mapping on top of each other, using a spectrum gradient as a base image.

#Gradient #Math #Maths #MathArt #Mathematical #MathematicalArt #Geometric #GeometricArt #GIMP #Rainbow #Rainbowcore #Psychedelia #Psychedelic #Spectrum #Colorful #Digital #DigitalArt #Abstract #AbstractArt #Art #Artwork #MastoArt #ArtistOnMastodon

Composition

Made by stacking multiple levels of composition of the rectangular-to-polar coordinate mapping on top of each other, using a spectrum gradient as a base image.

#Gradient #Math #Maths #MathArt #Mathematical #MathematicalArt #Geometric #GeometricArt #GIMP #Rainbow #Rainbowcore #Psychedelia #Psychedelic #Spectrum #Colorful #Digital #DigitalArt #Abstract #AbstractArt #Art #Artwork #MastoArt #ArtistOnMastodon

Linear Noise

Just made some more noise art for #Genuary . 😜

Noise art is a form of abstract art where an image is generated from statistical noise, where each pixel has a probability distribution as to what color it will be.

This artwork looks better if not zoomed in at 100%. Something about blending adjacent pixels together makes it look 3D.

#Generative #GenerativeArt #GenArtClub #MathArt #Mathematical #MathematicalArt #Geometric #GeometricArt #Neon #Rainbow #Colorful #Noise #Random

Linear Noise

Just made some more noise art for #Genuary . 😜

Noise art is a form of abstract art where an image is generated from statistical noise, where each pixel has a probability distribution as to what color it will be.

This artwork looks better if not zoomed in at 100%. Something about blending adjacent pixels together makes it look 3D.

#Generative #GenerativeArt #GenArtClub #MathArt #Mathematical #MathematicalArt #Geometric #GeometricArt #Neon #Rainbow #Colorful #Noise #Random

Some years ago I came up with a space-filling curve similar in spirit to the Hilbert curve, but triangular instead of square, and with smaller steps in the sequence of approximations. See here for the details: https://ideophilus.wordpress.com/2012/09/06/a-triangular-space-filling-curve/

Well, a commenter called Anthony D used the pattern for some floor tiles, and has given me permission to share photos, so here they are!

#fractal #fractals #maths #mathematics #MathematicalArt #mathsArt #mathArt #math

🌪️🌨️🌞🐺🖼️🖌️📸💻🐬☀️⛈️🌪️

🔥 LimitedEdition MetaPh Prints Available! 🔥

📩 DM to order directly from the artist — shipped to your door!

🌪️🌨️🌞🐺🖼️🖌️📸💻🐬☀️⛈️🌪️

MetaPh series by André Sier (since 2017)

📸 Moments captured through photography, enhanced by analog & mathematical lenses of imaginary arts. 🔍 Explore a world of metaphotography at: 👉 andre-sier.com/wolfanddotcom/metaph 👉 @a.sier

🌪️🌨️🌞🐺🖼️🖌️📸💻🐬☀️⛈️🌪️

✨ Tamanhos/Sizes (cm): 10x15, 40x30, 50x40, 70x50

📜 Papel / Paper: Semi-translúcido ou opaco matte 150g

🎨 Edition: 3 + PA / AP + PS / SP

🌪️🌨️🌞🐺🖼️🖌️📸💻🐬☀️⛈️🌪️

Série MetaPh de André Sier (desde 2017).

📸Momentos metafotográficos fixados através de fotografia ampliada com lentes analógicas e matemáticas de artes imaginárias. 🔍 Explora um mundo de metaphotografia: 👉 andre-sier.com/wolfanddotcom/metaph 👉 @a.sier

🌪️🌨️🌞🐺🖼️🖌️📸💻🐬☀️⛈️🌪️

🎯 Act fast! Secure your MetaPh print today!

#metaph #metaphotography #fractal #reality #nature #organism #viewingapparatus #lightmechanics #bliss #sea #light #imaging #exterior #world #abstract #art #photoart #imaginaryart #mathematicalart #computationalart #electronicart #digitalart #andrésier #originalartwork #edition3 #no_ai #sem_ia #andresier

see more @ https://www.instagram.com/a.sier/

Hybrid Manifold

Polar coordinate manipulation, made by combining the other three manifolds.

#Geometry #Geometric #GeometricArt #Abstract #AbstractArt #Mathematical #MathArt #MathsArt #MathematicalArt #GIMP #MadeWithGIMP #Digital #DigitalArt #Art #Artwork #Artist #MastoArt

Fire Manifold

Third installment in the Manifold series.

#Geometry #Geometric #GeometricArt #MathArt #MathsArt #Mathematical #MathematicalArt #Abstract #AbstractArt #Digital #DigitalArt #GIMP #MadeWithGIMP #Art #Artwork #Artist #MastoArt

Water Manifold

Another artwork in the manifold series. Created by mapping an image to polar coordinates multiple times in GIMP.

#Geometry #Geometric #GeometricArt #MathArt #Mathematical #MathematicalArt #Abstract #AbstractArt #Digital #DigitalArt #Water #Art #Artwork #Artist #MastoArt

Water Manifold

Another artwork in the manifold series. Created by mapping an image to polar coordinates multiple times in GIMP.

#Geometry #Geometric #GeometricArt #MathArt #Mathematical #MathematicalArt #Abstract #AbstractArt #Digital #DigitalArt #Water #Art #Artwork #Artist #MastoArt

Space Manifold

Artwork created by mapping an image to polar coordinates multiple times.

#Geometry #Geometric #GeometricArt #Abstract #AbstractArt #MathematicalArt #MathArt #MathsArt #DigitalArt #Art #Artwork #Artist #MastoArt

#MathematicalArt / #MathsArt / #MathArt picks of the day:

➡️ @gwenbeads - Maths teacher, artist & crafter

➡️ @ngons - Mathematical #geometric art by particle physicist / data scientist

➡️ @zenorogue - Creates indie games featuring #art inspired by #maths

➡️ @HypercubicPeg - Maths art using images, crochet, beading etc

➡️ @scdollins - Mathematically generated art & animations

➡️ @henryseg - 3D printed & CGI maths art

➡️ @benoitmandelbot - Bot posting images from Mandelbrot fractal

#MathematicalArt / #MathsArt / #MathArt picks of the day:

➡️ @gwenbeads - Maths teacher, artist & crafter

➡️ @ngons - Mathematical #geometric art by particle physicist / data scientist

➡️ @zenorogue - Creates indie games featuring #art inspired by #maths

➡️ @HypercubicPeg - Maths art using images, crochet, beading etc

➡️ @scdollins - Mathematically generated art & animations

➡️ @henryseg - 3D printed & CGI maths art

➡️ @benoitmandelbot - Bot posting images from Mandelbrot fractal

Newton fractal iteration
z - f(z)/f'(z) + c2

f(z) = z^-1-c
with c = (-1,0),
z initialized to (-1,0),
and c2 initialized to the coordinates for each point

#fractal #newtonFractal #mandelbrot #mathematicalArt

What's on your mind ?

#fractal #newtonFractal #mandelbrot #mathematicalArt

newton fractal iteration
z - f(z)/f'(z)

f(z) = z^3-z+c
(with z initialized to (0,0) and c initialized to the coordinates)

#fractal #newtonFractal #mandelbrot

What's on your mind ?

#fractal #newtonFractal #mandelbrot #mathematicalArt

newton fractal iteration
z - f(z)/f'(z)

f(z) = z^3-z+c
(with z initialized to (0,0) and c initialized to the coordinates)

#fractal #newtonFractal #mandelbrot

Newton fractal
z - a f(z)/f'(z)
f(z) = cos(z)^1-c with c = (0,0), a = (0.7,0)

#fractalArt #mathematicalArt
#fractal #genuary #genuary6 #newtonFractal

6/

In general, the smoothly-connecting double cusp groups with numerator k are clustered into groups where the denominator is of the form \(kn + m, m < k \); m, k co-prime.

So, for example:

- if k=4, m ϵ {1,3}
- if k=5, m ϵ {1,2,3,4}
- if k=6, m ϵ {1,5}
- if k=7, m ϵ {1,2,3,4,5,6}
- if k=8, m ϵ {1,3,5,7}

There are always an even number of such sub-streams, and they come in pairs (where m=j, k-j) where the structure is similar, but complementary. For example, when k=7, the paired streams are {7n+1, 7n+6}, {7n+2, 7n+5}, {7n+3, 7n+4}.

Attached are several movies that show this effect when the numerator is 7.

- the first one, titled "7n-Smoosh", shows what a concatenation looks like that includes all denominators in order, with maximum denominator 150

- the other three are titled "7n+1", "7n+2", and "7n+3" with maximum denominator 250

As was the case for the case where the numerator is 3, the relative beauty of these videos is in the eye of the beholder, but the ones that are constrained to constant offsets of a multiple of the numerator are much more consistent to one another.

#kleinianlimitset #kleiniangroup #fractals #mobius #mobiustransforms #mathematicalart #mathart #mastoart #perfectloops

5/

Attached are three different traces of the Maskit projection through the double-cusp groups where the numerator is 3, with a cap on the denominator at 188.

The first attached video (whose caption begins with "Smoosh") shows the result of concatenating every available cusp, sorted by increasing value of the corresponding fraction; that is, the cusp list starts with {3/188, 3/187, 3/185, 3/184 ...}. Note that there is no double-cusp group for 3/189 or 3/186 because those fractions reduce.

Unlike the movies for numerators 1 and 2, in this case the animation looks quite choppy and, although visual appeal is a matter of taste, certainly does not minimize differences between frames.

The second and third videos show the technique to generate smooth animations. Since the frames corresponding to cusps expressed as 3/(3n + 1) share an orientation, as do the cusps 3/(3n + 2), we must render two separate movies, one for each pattern, to get a smooth animation.

#kleinianlimitset #kleiniangroup #fractals #mobius #mobiustransforms #mathematicalart #mathart #mastoart #perfectloops

3/

The previous post showed an effect where color gradients for 1/n cusps are highly concentrated when n is a multiple of the palette size, and widely distributed when n is a half-multiple of the palette size. This effect appeared to be conserved across projections.

Attached are 4 images demonstrating that this effect appears to also be conserved under resizing the desired output image. I found this far more counter intuitive than conservation across projections -- after all, the value of ε is half as much as it was for the smaller renders, you'd expect that to affect the depth needed to get to a terminal node. Honestly, I don't have a great explanation for it; any actual topologists who want to weigh in with your two cents, please consider yourselves invited.

The attached still images are 1920x1080 and 960x540 renders of the Unit Circle projections of the 1/31 and 1/63 cusps; the larger ones have more detail, but still show the same color gradient distribution pattern.

The 1920x1080 animations are too large to host on Mastodon; the YouTube links follow; the only parameter changing between these and the animations posted earlier in this thread is the image size.

Jorgensen: https://youtu.be/lEY6yWwDT74

Unit Circle: https://youtu.be/Y1rczGsU9Hk

Maskit: https://youtu.be/CMb7OdDTH1o

Some of you (my favorites) are skeptically thinking "she's asserting that this happens on multiples and half-multiples of palette size, but she's only showing one of each."

Unit Circle Looping up to 1/189 cusp: https://youtu.be/mNRp74Pe8b4

Traversal in R, rendering using Cairo, movie conversion with ffmpeg.

#kleinianlimitset #kleiniangroup #fractals #mobius #mobiustransforms #mathematicalart #mathart #mastoart

2/

Attached see the same animations as in the first post in this thread, with the important exception that they are in different projections (the unit circle reference projection and the Maskit projection).

Just like the Jorgensen projection presented last time, these show the double cusp groups 1/n, where n is { 2, 3, 4, ... 63, 62, 61 ... 4, 3, 2 }. The palette (length 60) and color assignment rules similarly are the same.

At first it seems like quite a coincidence that the colors behave the same way with respect to n (that is, showing the most variation when n is a half-multiple of the palette size, the least when n is a multiple of the palette size), but it made sense (at least to me) after some reflection.

The underlying structure and topology of these projections are the same, so the node depth needed to draw what our minds perceive as the preserved elements from frame to frame proceeds the same way.

Interestingly, this phenomenon is conserved across resolutions as well, so renders of these groups at, say, 1920x1080, show the same high-level color patterning behavior (I'll post a demo later on YouTube).

Traversal in R, rendering using Cairo, movie conversion with ffmpeg.

#kleinianlimitset #kleiniangroup #fractals #mobius #mobiustransforms #mathematicalart #mathart #mastoart #perfectloops

1/

The next few posts are going to explore how to arrange limit sets in time to make movies that appeal to human eyes. So far the animations on this channel have varied granularity ε or the μ parameter that defines the topology of the limit set.

This movie, and the ones following in this thread, consists simply of concatenations of double cusp limit sets, so there is no continuous movement to model.

However, to our visual systems there is a "preferred" way to sequence double-cusp groups that is appealing, and conserved across projections.

The art tax for this post is a simple example of a pleasing path: a looped animation of the Jorgensen tb=2 projection for the cusps 1/n, where n is { 2, 3, 4, ... 63, 62, 61 ... 4, 3, 2 }.

The palette and the rules for choosing line colors (by the depth of the terminal node in the tree associated with those line segments) do not change at all from frame to frame. In this case the palette size was 60.

The apparent color-cycling behavior comes about because the shapes that our minds map as "the same" from one frame to the next have a consistently increasing tree depth associated with them.

To look at this a little more closely, see the attached still image, which shows how the structure of the limit set changes as n varies. Each step along the path is the transformation of the previous circle by a group generator. For the 1/n cusp, for walking this path, we apply the loxodromic/spiral generator a (or A) n times, before applying the parabolic generator B (or b).

Traversal in R, rendering using Cairo, movie conversion with ffmpeg.

#kleinianlimitset #kleiniangroup #fractals #mobius #mobiustransforms #mathematicalart #mathart #mastoart #perfectloops

This is the third in a series of posts arising from the Fibonacci cusps of Kleinian double-cusp groups.

As previously discussed, a series of fractions Fib(n)/Fib(n+1) will tend towards 1/ϕ over time. Correspondingly, the sequence of Fibonacci cusps on the Maskit curve will converge to the point corresponding to 1/ϕ, which generates what I suppose might be called the Golden Mean Group.

The μ parameter for this group for the Maskit slice where the second and fourth generators are parabolic ("tb=2") is provided in [1], specifically μ=1.2943265032+1.6168866453i (there is a mirror group with essentially the same properties at μ=0.7056734968+1.6168866453i). Curt McMullen and Troels Jorgensen were major proximate contributors to nailing this down.

Attached are Maskit and Jorgensen renders of the Golden Mean group. Interestingly, this set doesn't meet up like the Fib cusps that led up to it, even though the value of ε was set extremely low It looks like one of the intermediate frames from the walk animations, not a proper group. But what there still seems to be made up of tangent circles. What's going on? We'll start to explore that in the next post.

A completely different take on rendering this group is found in [1], fig 10.4 which is definitely worth a look if you're interested..

Traversal in R, rendering using Cairo, image editing in gimp.

[1] Mumford, D., Series, C., & Wright, D. (2002). Indra's Pearls: The Vision of Felix Klein. Cambridge: Cambridge University Press. doi:10.1017/CBO9781107050051

#kleinianlimitset #kleiniangroup #fractals #mobius #mobiustransforms #mathematicalart #generative #generativeart #mathart #fibonacci #fibonaccicusps

As scaffolding for a larger project, I had to figure out how to uniquely enumerate the generalized circles that make up any double-cusp Kleinian limit set, and determine their representative matrices.

Once I had my hands on that, it seemed natural to use those open interior spaces to recursively nest other limit sets.

The enclosing limit set is a 0/1 cusp displayed in the unit-circle reference projection described in _Indra's Pearls_. The nested limit sets were picked by starting at a random location in a large Farey sequence and simply using sequential elements.

The coloration comes from drawing the line segments based on how long the word associated with their corresponding terminal node is; this render used a palette of length 50, and flips the order of traversal at each nesting layer.

I wrote the rendering code in R, and rendered to .png using Cairo.

[1] Mumford, D., Series, C., & Wright, D. (2002). Indra's Pearls: The Vision of Felix Klein. Cambridge: Cambridge University Press. doi:10.1017/CBO9781107050051

#kleinianlimitset #kleiniangroup #fractals #mobius #mobiustransforms #mathematicalart #generative #generativeart

Having way too much fun making these little mini-fractals. Think I'll try printing on textured matte paper so they almost look like watercolors.

#minifractal #algorithmicart #mathematicalart #artmath

Noise Bullseye

Experimenting with semi-random noise in Processing. In this generative art piece I programmed it so that each pixel has a random lightness and the lightness is biased towards a certain value. That value is determined by the sine function, which is plotted in polar coordinates.

You'll notice that there are rings of pure black... This is due to the value of the sine function being zero (I used sin( r/20 ) + 1 so the the area where the sine is zero is stretched out) and the fact that the lightness of each pixel is obtained by multiplying by the sine function. So the lightness of these pixels is a random value multiplied by the sine at that location, which ends up being zero.

I like how the result ended up looking like a 3D styrofoam bullseye.

#Art #ArtistOfMastodon #Abstract #AbstractArt #Generative #GenerativeArt #Math #MathArt #Maths #Mathematics #MathematicalArt #Geometry #Geometric #GeometricArt #Coding #Programming #Algorithm #Processing