#algorist — Public Fediverse posts

It was twenty years ago today
Sam L Jackson fought the snakes in air
They've been going in and out of memes
Guess they're funny if you're in your teens
So may I just remind you of
The act you've known for all these years
Monty Python's "Hovercraft full of eels".

#snakesonaplane #myhovercraftisfullofeels

#digitaldoodle #meander #matopeli #creepycrawly #wiggle #slither #pythoncode #opengl #algorithmicart #algorist #creativecoding #artxcode #computerart #ittaide #kuavataide #iterati

I've been playing with a very simple approach to meandering paths. I'm not sure if I'm getting anywhere with these, but I thought I'd post some of the tests so far.

The problem with the 2D idea is that the paths will easily wander off the screen. So I thought I'd put them on a spherical surface to contain them. It turned out this isn't quite trivial, and I had to rethink what directions and turns actually mean there. It all came down to the Non-Euclidean nature of the sphere. A straight-line direction there means a great circle, but no two great circles can be parallel. So directions and positions are rather closely linked. This is in contrast to Euclidean geometry, where you can go from any point into any direction.

#meander #matopeli #creepycrawly #wiggle #slither #pythoncode #opengl #algorithmicart #algorist #creativecoding #artxcode #computerart #ittaide #kuavataide #iterati

More wriggling motions in the plasma-globe-inspired demo. I also added periodic resets to further mess things up.

#plasmaglobe #plasma #particlesimulation #pythoncode #opengl #vertexshader #algorithmicart #algorist #creativecoding #artxcode #computerart #ittaide #kuavataide #iterati

It's been quiet on the demo front as my musician side has recently taken over. This slow return to musicianship started last summer, with the new twist of using the Karelian language. I've also put some of my old and new demos to work for the music videos. Here's the latest piece by me and Noira, you'll find a couple more on the same Salixvelox channel:

https://youtu.be/XI9XJKDMd3k

#karelianlanguage #karelianproper #southkarelian #karjalankieli #karjalankielieläy #varzinkarjala #suvikarjala #opengl #pythoncode #algorithmicart #algorist #creativecoding #artxcode #computerart #ittaide #kuavataide #iterati

Following my recent 2D image morphing demos, I've been thinking of visualizing the process as a single 3D shape. Since it starts with pixelated images, a voxel approach seemed the most straightforward.

While I wasn't quite happy with the blocky look, the parallel columns of voxels caught my attention, and they became a key stylistic element; they reminded me of the "fibre optic" mineral ulexite. I imagined carving a sculpture of such a fibrous material. So I replaced the piecewise columns by these long tubes.

Fox drawing courtesy of @noira_musti

#morphing #3dgraphics #digitalsculpture #pythoncode #numpy #opengl #algorithmicart #algorist

From a pile of shit, new life grows. Conway's Game of Life running independently in the 3 colour channels in 64x64 cells with wrap-around topology.

Not much new code here, just added image loading capability to my old pile-up demo of 2D cellular automata.

#cellularautomaton #gameoflife #conwaysgameoflife #pixelart #voxelart #blockart #3dgraphics #opengl #pythoncode #numpy #algorithmicart #algorist #creativecoding #artxcode #computerart #ittaide #kuavataide #iterati

A basic algorithm for a basic guy: find the edge points in the binary image and change their colour to that of the target image. Rinse and repeat until the edge no longer moves.

#trumpmemes #donaldtrump #greenland #makeamericagreenlandagain #trumpland #cellularautomaton #edgedetection #vonneumann #pythoncode #opengl #algorithmicart #algorist

Highlights of the year

#highlighter #trumpmemes #epsteinmemes #jeffreyepstein #epsteinfiles #halftoneart #raster #pixelart #textmode #textmodeart #ansiart #oldskool #xterm #pythoncode #algorithmicart #algorist

New Year's Redactions

My earlier text redaction demos were done in my OpenGL setup, using a pixelation effect overlaid on a text document. This was rather simple, but it required some manual tweaking to align the pixelation grid with the text. I've now redone the effect in text mode using Python, and besides unifying the text and "graphics" more cleanly, it makes certain extra features easier, such as this incremental redaction. Of course, video sources as used in the previous post also work.

A particular feature of the unified text + graphics process is that redactions won't exceed the length of each line. In the OpenGL version, the draw area had to be limited to the text rectangle manually, but now it works as it should have done all along.

#2026 #trumpmemes #epsteinmemes #jeffreyepstein #epsteinfiles #halftoneart #raster #pixelart #textmode #textmodeart #oldskool #xterm #pythoncode #algorithmicart #algorist

What shall we find in the Epstein files?
What shall we find in the Epstein files?
What shall we find in the Epstein files
early in the morning?

Model: @noira_musti

#trumpmemes #epsteinmemes #jeffreyepstein #epsteinfiles #halftoneart #raster #pixelart #realtime #opengl #pythoncode #algorithmicart #algorist

What shall we find in the Epstein files?
What shall we find in the Epstein files?
What shall we find in the Epstein files
early in the morning?

Model: @noira_musti

#trumpmemes #epsteinmemes #jeffreyepstein #epsteinfiles #halftoneart #raster #pixelart #realtime #opengl #pythoncode #algorithmicart #algorist

What shall we find in the Epstein files?
What shall we find in the Epstein files?
What shall we find in the Epstein files
early in the morning?

Model: @noira_musti

#trumpmemes #epsteinmemes #jeffreyepstein #epsteinfiles #halftoneart #raster #pixelart #realtime #opengl #pythoncode #algorithmicart #algorist

What shall we find in the Epstein files?
What shall we find in the Epstein files?
What shall we find in the Epstein files
early in the morning?

Model: @noira_musti

#trumpmemes #epsteinmemes #jeffreyepstein #epsteinfiles #halftoneart #raster #pixelart #realtime #opengl #pythoncode #algorithmicart #algorist

What shall we find in the Epstein files?
What shall we find in the Epstein files?
What shall we find in the Epstein files
early in the morning?

Model: @noira_musti

#trumpmemes #epsteinmemes #jeffreyepstein #epsteinfiles #halftoneart #raster #pixelart #realtime #opengl #pythoncode #algorithmicart #algorist

Trump found in the Epstein files! A little Xmas fun with image quantization.

#donaldtrump #trumpmemes #jeffreyepstein #epsteinfiles #halftoneart #raster #pixelart #algorithmicart #algorist

Rule/Yule 30 cellular automaton with a "band-pass" filter every few iterations. Done in the Bash shell using bitwise math, so each row/state is a single number of 63 bits.

#cellularautomata #cellularautomaton #rule30 #bitwiseoperators #textmode #textmodeart #oldskool #retrocomputing #unixshell #shellprogramming #xterm #joulu6 #xmastree #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Rule/Yule 30 cellular automaton with a "band-pass" filter every few iterations. Done in the Bash shell using bitwise math, so each row/state is a single number of 63 bits.

#cellularautomata #cellularautomaton #rule30 #bitwiseoperators #textmode #textmodeart #oldskool #retrocomputing #unixshell #shellprogramming #xterm #joulu6 #xmastree #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Rule/Yule 30 cellular automaton with a "band-pass" filter every few iterations. Done in the Bash shell using bitwise math, so each row/state is a single number of 63 bits.

#cellularautomata #cellularautomaton #rule30 #bitwiseoperators #textmode #textmodeart #oldskool #retrocomputing #unixshell #shellprogramming #xterm #joulu6 #xmastree #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Rule/Yule 30 cellular automaton with a "band-pass" filter every few iterations. Done in the Bash shell using bitwise math, so each row/state is a single number of 63 bits.

#cellularautomata #cellularautomaton #rule30 #bitwiseoperators #textmode #textmodeart #oldskool #retrocomputing #unixshell #shellprogramming #xterm #joulu6 #xmastree #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Rule/Yule 30 cellular automaton with a "band-pass" filter every few iterations. Done in the Bash shell using bitwise math, so each row/state is a single number of 63 bits.

#cellularautomata #cellularautomaton #rule30 #bitwiseoperators #textmode #textmodeart #oldskool #retrocomputing #unixshell #shellprogramming #xterm #joulu6 #xmastree #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Sierpinski triangles on an icosahedron, inspired by Ghee Beom Kim

#sierpinskitriangle #icosahedron #geometricart #fractal #fractalart #iteratedfunctionsystem #3dgraphics #raymarching #pythoncode #numpy #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Sierpinski triangles on an icosahedron, inspired by Ghee Beom Kim

#sierpinskitriangle #icosahedron #geometricart #fractal #fractalart #iteratedfunctionsystem #3dgraphics #raymarching #pythoncode #numpy #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Sierpinski triangles on an icosahedron, inspired by Ghee Beom Kim

#sierpinskitriangle #icosahedron #geometricart #fractal #fractalart #iteratedfunctionsystem #3dgraphics #raymarching #pythoncode #numpy #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Another blow-up view of the Apollonian spheres, now dropping on a concave surface to gather all the jetsam together. This is what I had in mind when writing the first drop demo, and the model just needed a bit of refinement for the differently sized balls: properly scaled masses and elastic factors, as well as proper handling of these quantities in each pair collision.

As a recovering science teacher, it's fun to see such physics in action: a simple, linear elastic force is all it takes to keep each body in its place. Well, at least approximately; I've included a basic drag term to help things settle, but it seems it would take a while, as the tiniest balls are easily thrown around by the larger masses.

#apollonianspheres #apolloniangasket #particlesimulation #elasticcollision #hookeslaw #3dgraphics #pythoncode #numpy #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

With 2D Apollonian gaskets, it's easy to build arbitrary initial configurations. Simply picking 3 random points means you have to solve for 3 radii to make a kissing setup. Since there are exactly 3 distances between the points, this makes a basic linear system. But not so in 3D: you have 4 points and 4 radii, but 6 different distances, so a linear solution won't cut it. You could start with 3 kissing spheres using the 2D logic, but then you can't put the 4th point just anywhere.

I didn't bother with the messy quadratic system, because there's an easier way: take the symmetric tetrahedral config and deform it using an inversion. Yep, the same tool that's already the bread and butter of gasket-weaving. What's more, we can build the symmetric gasket first and then deform the whole thing. Inversion preserves spheres as spheres and maintains their kissing relations, it doesn't care how many there are.

In other words, the order doesn't matter with inversions. I've used this trick years ago in some 2D inversion demos to simplify things, and this 3D also benefits hugely from it. Besides the problem of initial config, 3D gaskets also have a speed issue due to deduplication (explained in an earlier post). The inversions are very fast as they can be parallelized, and this also applies to the deformations. So it's nice that we need not rebuild the gasket again for every config, we can just deform the same thing again.

#apollonianspheres #apolloniangasket #gasketweaving #iteratedfunctionsystem #inversion #sphereinversion #geometricart #3dgraphics #digitalsculpture #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

With 2D Apollonian gaskets, it's easy to build arbitrary initial configurations. Simply picking 3 random points means you have to solve for 3 radii to make a kissing setup. Since there are exactly 3 distances between the points, this makes a basic linear system. But not so in 3D: you have 4 points and 4 radii, but 6 different distances, so a linear solution won't cut it. You could start with 3 kissing spheres using the 2D logic, but then you can't put the 4th point just anywhere.

I didn't bother with the messy quadratic system, because there's an easier way: take the symmetric tetrahedral config and deform it using an inversion. Yep, the same tool that's already the bread and butter of gasket-weaving. What's more, we can build the symmetric gasket first and then deform the whole thing. Inversion preserves spheres as spheres and maintains their kissing relations, it doesn't care how many there are.

In other words, the order doesn't matter with inversions. I've used this trick years ago in some 2D inversion demos to simplify things, and this 3D also benefits hugely from it. Besides the problem of initial config, 3D gaskets also have a speed issue due to deduplication (explained in an earlier post). The inversions are very fast as they can be parallelized, and this also applies to the deformations. So it's nice that we need not rebuild the gasket again for every config, we can just deform the same thing again.

#apollonianspheres #apolloniangasket #gasketweaving #iteratedfunctionsystem #inversion #sphereinversion #geometricart #3dgraphics #digitalsculpture #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

With 2D Apollonian gaskets, it's easy to build arbitrary initial configurations. Simply picking 3 random points means you have to solve for 3 radii to make a kissing setup. Since there are exactly 3 distances between the points, this makes a basic linear system. But not so in 3D: you have 4 points and 4 radii, but 6 different distances, so a linear solution won't cut it. You could start with 3 kissing spheres using the 2D logic, but then you can't put the 4th point just anywhere.

I didn't bother with the messy quadratic system, because there's an easier way: take the symmetric tetrahedral config and deform it using an inversion. Yep, the same tool that's already the bread and butter of gasket-weaving. What's more, we can build the symmetric gasket first and then deform the whole thing. Inversion preserves spheres as spheres and maintains their kissing relations, it doesn't care how many there are.

In other words, the order doesn't matter with inversions. I've used this trick years ago in some 2D inversion demos to simplify things, and this 3D also benefits hugely from it. Besides the problem of initial config, 3D gaskets also have a speed issue due to deduplication (explained in an earlier post). The inversions are very fast as they can be parallelized, and this also applies to the deformations. So it's nice that we need not rebuild the gasket again for every config, we can just deform the same thing again.

#apollonianspheres #apolloniangasket #gasketweaving #iteratedfunctionsystem #inversion #sphereinversion #geometricart #3dgraphics #digitalsculpture #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

With 2D Apollonian gaskets, it's easy to build arbitrary initial configurations. Simply picking 3 random points means you have to solve for 3 radii to make a kissing setup. Since there are exactly 3 distances between the points, this makes a basic linear system. But not so in 3D: you have 4 points and 4 radii, but 6 different distances, so a linear solution won't cut it. You could start with 3 kissing spheres using the 2D logic, but then you can't put the 4th point just anywhere.

I didn't bother with the messy quadratic system, because there's an easier way: take the symmetric tetrahedral config and deform it using an inversion. Yep, the same tool that's already the bread and butter of gasket-weaving. What's more, we can build the symmetric gasket first and then deform the whole thing. Inversion preserves spheres as spheres and maintains their kissing relations, it doesn't care how many there are.

In other words, the order doesn't matter with inversions. I've used this trick years ago in some 2D inversion demos to simplify things, and this 3D also benefits hugely from it. Besides the problem of initial config, 3D gaskets also have a speed issue due to deduplication (explained in an earlier post). The inversions are very fast as they can be parallelized, and this also applies to the deformations. So it's nice that we need not rebuild the gasket again for every config, we can just deform the same thing again.

#apollonianspheres #apolloniangasket #gasketweaving #iteratedfunctionsystem #inversion #sphereinversion #geometricart #3dgraphics #digitalsculpture #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

With 2D Apollonian gaskets, it's easy to build arbitrary initial configurations. Simply picking 3 random points means you have to solve for 3 radii to make a kissing setup. Since there are exactly 3 distances between the points, this makes a basic linear system. But not so in 3D: you have 4 points and 4 radii, but 6 different distances, so a linear solution won't cut it. You could start with 3 kissing spheres using the 2D logic, but then you can't put the 4th point just anywhere.

I didn't bother with the messy quadratic system, because there's an easier way: take the symmetric tetrahedral config and deform it using an inversion. Yep, the same tool that's already the bread and butter of gasket-weaving. What's more, we can build the symmetric gasket first and then deform the whole thing. Inversion preserves spheres as spheres and maintains their kissing relations, it doesn't care how many there are.

In other words, the order doesn't matter with inversions. I've used this trick years ago in some 2D inversion demos to simplify things, and this 3D also benefits hugely from it. Besides the problem of initial config, 3D gaskets also have a speed issue due to deduplication (explained in an earlier post). The inversions are very fast as they can be parallelized, and this also applies to the deformations. So it's nice that we need not rebuild the gasket again for every config, we can just deform the same thing again.

#apollonianspheres #apolloniangasket #gasketweaving #iteratedfunctionsystem #inversion #sphereinversion #geometricart #3dgraphics #digitalsculpture #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Making Apollonian gaskets usually follows a key rule of iterated function systems: each iteration should make the thing smaller. With inversions, this means going from the outside to the inside of inverting circles.

However, it's possible to make valid gaskets using a lopsided configuration, where the initial circles are bunched up on one side. In that case, the first iteration has to make a larger circle to fill the opposite side. This means an inversion from the inside to outside. But we can also think of this as turning the inversion circle inside out.

This turns out nice both visually and conceptually. An inversion circle is essentially a curved mirror, and we can make a smooth transition from the convex to the concave by passing through the flat stage. I wasn't sure if this would work cleanly in this simple demo, since the flat mirror means a circle with infinite radius; fortunately, the finite time steps mean we can skip over the flat point.

As for IFS rules, the system as a whole is contractive, thanks to the other circles that are now more convex.

The second part gives another look at such initially lopsided gaskets.

#apolloniancircles #apolloniangasket #iteratedfunctionsystem #inversion #circleinversion #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Making Apollonian gaskets usually follows a key rule of iterated function systems: each iteration should make the thing smaller. With inversions, this means going from the outside to the inside of inverting circles.

However, it's possible to make valid gaskets using a lopsided configuration, where the initial circles are bunched up on one side. In that case, the first iteration has to make a larger circle to fill the opposite side. This means an inversion from the inside to outside. But we can also think of this as turning the inversion circle inside out.

This turns out nice both visually and conceptually. An inversion circle is essentially a curved mirror, and we can make a smooth transition from the convex to the concave by passing through the flat stage. I wasn't sure if this would work cleanly in this simple demo, since the flat mirror means a circle with infinite radius; fortunately, the finite time steps mean we can skip over the flat point.

As for IFS rules, the system as a whole is contractive, thanks to the other circles that are now more convex.

The second part gives another look at such initially lopsided gaskets.

#apolloniancircles #apolloniangasket #iteratedfunctionsystem #inversion #circleinversion #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Making Apollonian gaskets usually follows a key rule of iterated function systems: each iteration should make the thing smaller. With inversions, this means going from the outside to the inside of inverting circles.

However, it's possible to make valid gaskets using a lopsided configuration, where the initial circles are bunched up on one side. In that case, the first iteration has to make a larger circle to fill the opposite side. This means an inversion from the inside to outside. But we can also think of this as turning the inversion circle inside out.

This turns out nice both visually and conceptually. An inversion circle is essentially a curved mirror, and we can make a smooth transition from the convex to the concave by passing through the flat stage. I wasn't sure if this would work cleanly in this simple demo, since the flat mirror means a circle with infinite radius; fortunately, the finite time steps mean we can skip over the flat point.

As for IFS rules, the system as a whole is contractive, thanks to the other circles that are now more convex.

The second part gives another look at such initially lopsided gaskets.

#apolloniancircles #apolloniangasket #iteratedfunctionsystem #inversion #circleinversion #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Making Apollonian gaskets usually follows a key rule of iterated function systems: each iteration should make the thing smaller. With inversions, this means going from the outside to the inside of inverting circles.

However, it's possible to make valid gaskets using a lopsided configuration, where the initial circles are bunched up on one side. In that case, the first iteration has to make a larger circle to fill the opposite side. This means an inversion from the inside to outside. But we can also think of this as turning the inversion circle inside out.

This turns out nice both visually and conceptually. An inversion circle is essentially a curved mirror, and we can make a smooth transition from the convex to the concave by passing through the flat stage. I wasn't sure if this would work cleanly in this simple demo, since the flat mirror means a circle with infinite radius; fortunately, the finite time steps mean we can skip over the flat point.

As for IFS rules, the system as a whole is contractive, thanks to the other circles that are now more convex.

The second part gives another look at such initially lopsided gaskets.

#apolloniancircles #apolloniangasket #iteratedfunctionsystem #inversion #circleinversion #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Making Apollonian gaskets usually follows a key rule of iterated function systems: each iteration should make the thing smaller. With inversions, this means going from the outside to the inside of inverting circles.

However, it's possible to make valid gaskets using a lopsided configuration, where the initial circles are bunched up on one side. In that case, the first iteration has to make a larger circle to fill the opposite side. This means an inversion from the inside to outside. But we can also think of this as turning the inversion circle inside out.

This turns out nice both visually and conceptually. An inversion circle is essentially a curved mirror, and we can make a smooth transition from the convex to the concave by passing through the flat stage. I wasn't sure if this would work cleanly in this simple demo, since the flat mirror means a circle with infinite radius; fortunately, the finite time steps mean we can skip over the flat point.

As for IFS rules, the system as a whole is contractive, thanks to the other circles that are now more convex.

The second part gives another look at such initially lopsided gaskets.

#apolloniancircles #apolloniangasket #iteratedfunctionsystem #inversion #circleinversion #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Another look at Apollonian spheres, cutting out the top half and showing a few iteration steps.

#apollonianspheres #apolloniangasket #iteratedfunctionsystem #inversion #sphereinversion #geometricart #3dgraphics #digitalsculpture #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Another look at Apollonian spheres, cutting out the top half and showing a few iteration steps.

#apollonianspheres #apolloniangasket #iteratedfunctionsystem #inversion #sphereinversion #geometricart #3dgraphics #digitalsculpture #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Another look at Apollonian spheres, cutting out the top half and showing a few iteration steps.

#apollonianspheres #apolloniangasket #iteratedfunctionsystem #inversion #sphereinversion #geometricart #3dgraphics #digitalsculpture #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Another look at Apollonian spheres, cutting out the top half and showing a few iteration steps.

#apollonianspheres #apolloniangasket #iteratedfunctionsystem #inversion #sphereinversion #geometricart #3dgraphics #digitalsculpture #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Another look at Apollonian spheres, cutting out the top half and showing a few iteration steps.

#apollonianspheres #apolloniangasket #iteratedfunctionsystem #inversion #sphereinversion #geometricart #3dgraphics #digitalsculpture #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Taking my lastest Apollonian gasket code from 2D to 3D was quite straightforward in principle, though there were a few kinks in the road. A particular difference between 2D and 3D gaskets is that in 3D, the inversion spheres overlap, which can create duplicate spheres.

Viewing detailed 3D structures isn't trivial either. We can only really see in 2D, as one dimension is taken up by the ray of light. Looking from outside, I wouldn't guess this blob contains over 10k spheres, so I blew it up for this clip.

The sheer amount of balls is also heavy on the drawing side, so I used my low-poly "sprites" where each ball is drawn by a geometry shader from a single input point. The low-poly aspect is quite clear in the largest spheres, but I think it's OK for this math demo.

#apollonianspheres #apolloniangasket #iteratedfunctionsystem #inversion #sphereinversion #geometricart #3dgraphics #digitalsculpture #pythoncode #opengl #geometryshader #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Taking my lastest Apollonian gasket code from 2D to 3D was quite straightforward in principle, though there were a few kinks in the road. A particular difference between 2D and 3D gaskets is that in 3D, the inversion spheres overlap, which can create duplicate spheres.

Viewing detailed 3D structures isn't trivial either. We can only really see in 2D, as one dimension is taken up by the ray of light. Looking from outside, I wouldn't guess this blob contains over 10k spheres, so I blew it up for this clip.

The sheer amount of balls is also heavy on the drawing side, so I used my low-poly "sprites" where each ball is drawn by a geometry shader from a single input point. The low-poly aspect is quite clear in the largest spheres, but I think it's OK for this math demo.

#apollonianspheres #apolloniangasket #iteratedfunctionsystem #inversion #sphereinversion #geometricart #3dgraphics #digitalsculpture #pythoncode #opengl #geometryshader #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Taking my lastest Apollonian gasket code from 2D to 3D was quite straightforward in principle, though there were a few kinks in the road. A particular difference between 2D and 3D gaskets is that in 3D, the inversion spheres overlap, which can create duplicate spheres.

Viewing detailed 3D structures isn't trivial either. We can only really see in 2D, as one dimension is taken up by the ray of light. Looking from outside, I wouldn't guess this blob contains over 10k spheres, so I blew it up for this clip.

The sheer amount of balls is also heavy on the drawing side, so I used my low-poly "sprites" where each ball is drawn by a geometry shader from a single input point. The low-poly aspect is quite clear in the largest spheres, but I think it's OK for this math demo.

#apollonianspheres #apolloniangasket #iteratedfunctionsystem #inversion #sphereinversion #geometricart #3dgraphics #digitalsculpture #pythoncode #opengl #geometryshader #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Taking my lastest Apollonian gasket code from 2D to 3D was quite straightforward in principle, though there were a few kinks in the road. A particular difference between 2D and 3D gaskets is that in 3D, the inversion spheres overlap, which can create duplicate spheres.

Viewing detailed 3D structures isn't trivial either. We can only really see in 2D, as one dimension is taken up by the ray of light. Looking from outside, I wouldn't guess this blob contains over 10k spheres, so I blew it up for this clip.

The sheer amount of balls is also heavy on the drawing side, so I used my low-poly "sprites" where each ball is drawn by a geometry shader from a single input point. The low-poly aspect is quite clear in the largest spheres, but I think it's OK for this math demo.

#apollonianspheres #apolloniangasket #iteratedfunctionsystem #inversion #sphereinversion #geometricart #3dgraphics #digitalsculpture #pythoncode #opengl #geometryshader #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

Taking my lastest Apollonian gasket code from 2D to 3D was quite straightforward in principle, though there were a few kinks in the road. A particular difference between 2D and 3D gaskets is that in 3D, the inversion spheres overlap, which can create duplicate spheres.

Viewing detailed 3D structures isn't trivial either. We can only really see in 2D, as one dimension is taken up by the ray of light. Looking from outside, I wouldn't guess this blob contains over 10k spheres, so I blew it up for this clip.

The sheer amount of balls is also heavy on the drawing side, so I used my low-poly "sprites" where each ball is drawn by a geometry shader from a single input point. The low-poly aspect is quite clear in the largest spheres, but I think it's OK for this math demo.

#apollonianspheres #apolloniangasket #iteratedfunctionsystem #inversion #sphereinversion #geometricart #3dgraphics #digitalsculpture #pythoncode #opengl #geometryshader #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

As I keep studying the Apollonian gasket, I've now implemented the inversion approach on the CPU for finding the circle centres and radii. Now I can generate these arrays of eyes much faster, as the inversion is easier to parallelize. It's so fast that the bottleneck is now in the drawing stage.

The colours denote a kind of family tree of inversions: the 4 initial circles each have their own colour, and their inversion images retain the colour. The outer circle is not shown here, but its descendants show the colour that's distinct from the other 3.

I still needed something other than inversions for setting up the initial quartet, but I wanted find my own solution instead of relying on Descartes' theorem. The theorem actually comes in two parts: Rene's original theorem only deals with the radii, while the complex quadratic formula for finding the circle positions was only developed in the late 1990s.

Well, I found an alternative solution to the latter part, and it reduces to a pair of linear equations. It isn't particularly fast to compute, but I think it's easier to understand — it's basically junior high school math. In fact, it seems so basic that I can't be the first one to discover it.

#eyecandy #apolloniancircles #apolloniangasket #iteratedfunctionsystem #inversion #circleinversion #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

As I keep studying the Apollonian gasket, I've now implemented the inversion approach on the CPU for finding the circle centres and radii. Now I can generate these arrays of eyes much faster, as the inversion is easier to parallelize. It's so fast that the bottleneck is now in the drawing stage.

The colours denote a kind of family tree of inversions: the 4 initial circles each have their own colour, and their inversion images retain the colour. The outer circle is not shown here, but its descendants show the colour that's distinct from the other 3.

I still needed something other than inversions for setting up the initial quartet, but I wanted find my own solution instead of relying on Descartes' theorem. The theorem actually comes in two parts: Rene's original theorem only deals with the radii, while the complex quadratic formula for finding the circle positions was only developed in the late 1990s.

Well, I found an alternative solution to the latter part, and it reduces to a pair of linear equations. It isn't particularly fast to compute, but I think it's easier to understand — it's basically junior high school math. In fact, it seems so basic that I can't be the first one to discover it.

#eyecandy #apolloniancircles #apolloniangasket #iteratedfunctionsystem #inversion #circleinversion #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

As I keep studying the Apollonian gasket, I've now implemented the inversion approach on the CPU for finding the circle centres and radii. Now I can generate these arrays of eyes much faster, as the inversion is easier to parallelize. It's so fast that the bottleneck is now in the drawing stage.

The colours denote a kind of family tree of inversions: the 4 initial circles each have their own colour, and their inversion images retain the colour. The outer circle is not shown here, but its descendants show the colour that's distinct from the other 3.

I still needed something other than inversions for setting up the initial quartet, but I wanted find my own solution instead of relying on Descartes' theorem. The theorem actually comes in two parts: Rene's original theorem only deals with the radii, while the complex quadratic formula for finding the circle positions was only developed in the late 1990s.

Well, I found an alternative solution to the latter part, and it reduces to a pair of linear equations. It isn't particularly fast to compute, but I think it's easier to understand — it's basically junior high school math. In fact, it seems so basic that I can't be the first one to discover it.

#eyecandy #apolloniancircles #apolloniangasket #iteratedfunctionsystem #inversion #circleinversion #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

As I keep studying the Apollonian gasket, I've now implemented the inversion approach on the CPU for finding the circle centres and radii. Now I can generate these arrays of eyes much faster, as the inversion is easier to parallelize. It's so fast that the bottleneck is now in the drawing stage.

The colours denote a kind of family tree of inversions: the 4 initial circles each have their own colour, and their inversion images retain the colour. The outer circle is not shown here, but its descendants show the colour that's distinct from the other 3.

I still needed something other than inversions for setting up the initial quartet, but I wanted find my own solution instead of relying on Descartes' theorem. The theorem actually comes in two parts: Rene's original theorem only deals with the radii, while the complex quadratic formula for finding the circle positions was only developed in the late 1990s.

Well, I found an alternative solution to the latter part, and it reduces to a pair of linear equations. It isn't particularly fast to compute, but I think it's easier to understand — it's basically junior high school math. In fact, it seems so basic that I can't be the first one to discover it.

#eyecandy #apolloniancircles #apolloniangasket #iteratedfunctionsystem #inversion #circleinversion #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

As I keep studying the Apollonian gasket, I've now implemented the inversion approach on the CPU for finding the circle centres and radii. Now I can generate these arrays of eyes much faster, as the inversion is easier to parallelize. It's so fast that the bottleneck is now in the drawing stage.

The colours denote a kind of family tree of inversions: the 4 initial circles each have their own colour, and their inversion images retain the colour. The outer circle is not shown here, but its descendants show the colour that's distinct from the other 3.

I still needed something other than inversions for setting up the initial quartet, but I wanted find my own solution instead of relying on Descartes' theorem. The theorem actually comes in two parts: Rene's original theorem only deals with the radii, while the complex quadratic formula for finding the circle positions was only developed in the late 1990s.

Well, I found an alternative solution to the latter part, and it reduces to a pair of linear equations. It isn't particularly fast to compute, but I think it's easier to understand — it's basically junior high school math. In fact, it seems so basic that I can't be the first one to discover it.

#eyecandy #apolloniancircles #apolloniangasket #iteratedfunctionsystem #inversion #circleinversion #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

2D circle inversion fractals on the spherical surface. This was a fun offshoot of my recent Apollonian endeavours, again using the Riemann sphere mapping to go from 3D to 2D for the iterations.

The inversion circle centres come from a tetrakis hexahedron and a triakis icosahedron, so the circles form approximations of a truncated octahedron and a truncated dodecahedron.

#apolloniancircles #apolloniangasket #inversion #circleinversion #riemannsphere #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati