#kuavataide — Public Fediverse posts

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

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

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

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

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

The set of polyhedra that can be converted into Apollonian gaskets via sphere-plane mapping is quite limited. The face polygons should be regular, the edge midpoints should all lie on the same sphere, and the vertices should be 3-fold. There are some Platonic solids that work, and I've showed all of these earlier. It turns out that Archimedean solids with 3-fold vertices work too. So here's a truncated octahedron, also showing a progressive view of the gasket iteration.

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

The set of polyhedra that can be converted into Apollonian gaskets via sphere-plane mapping is quite limited. The face polygons should be regular, the edge midpoints should all lie on the same sphere, and the vertices should be 3-fold. There are some Platonic solids that work, and I've showed all of these earlier. It turns out that Archimedean solids with 3-fold vertices work too. So here's a truncated octahedron, also showing a progressive view of the gasket iteration.

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

The set of polyhedra that can be converted into Apollonian gaskets via sphere-plane mapping is quite limited. The face polygons should be regular, the edge midpoints should all lie on the same sphere, and the vertices should be 3-fold. There are some Platonic solids that work, and I've showed all of these earlier. It turns out that Archimedean solids with 3-fold vertices work too. So here's a truncated octahedron, also showing a progressive view of the gasket iteration.

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

The set of polyhedra that can be converted into Apollonian gaskets via sphere-plane mapping is quite limited. The face polygons should be regular, the edge midpoints should all lie on the same sphere, and the vertices should be 3-fold. There are some Platonic solids that work, and I've showed all of these earlier. It turns out that Archimedean solids with 3-fold vertices work too. So here's a truncated octahedron, also showing a progressive view of the gasket iteration.

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

Apollonian gaskets based on Platonic solids. The vertices of a tetrahedron/octahedron/icosahedron are used for the centre positions of the initial circles. These are Riemann-sphere-mapped to the complex plane, where the gasket is iterated for more circles, and the result is mapped back onto the sphere. It's a little roundabout, but it works for me, and the heaviest part by far is drawing the visuals.

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

Riemann sphere mappings of Apollonian gaskets. After the 2D gaskets, I'd been thinking of some kind of 3D versions for a while, but the final inspiration came from Antti Immonen's sculptures I saw on Friday at the opening of his exhibition here in Jyväskylä. As a real-life sculptor who incorporates fractals and other math ideas in his works, he's a pretty rare specimen at least by national standards.

Since my 2D gaskets are fitted to the unit circle, they cover exactly half of the Riemann sphere, as seen in the first part. My lazy solution to covering the entire sphere was a simple copy-paste, and the result doesn't seem too bad.

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

The previous demo made me dig deeper into dithering algorithms. It's something I should have done years ago, as I've been using simple random dithering now and then, and I hadn't even thought of gamma correction. One algorithm in particular caught my eye: Riemersma dithering, which uses the Hilbert curve. Compared to the usual matrices for error diffusion, the curve approach seemed easier to implement in some ways, as it has fewer edge issues.

More interestingly, it struck a chord with my earlier experiments with space-filling curves in image processing. So it was a kind of familiar territory, but it also seemed esoteric enough that I could imagine making some new discoveries. For example, play with other plane-filling curves besides the Hilbert.

The first image uses the boustrophedon curve, which makes the vertical wave patterns I recall from a number of non-dithering demos. The second curve is what I call the diagstrophedon, a diagonal zig-zag starting from the top left corner, and I think its wavy artefacts make a nice match for Venus's hair.

Then in image 3 we have Hilbert, which doesn't seem to make any particular artefacts, and I guess that's a good thing for dithering. Finally 4 uses the Peano curve, which makes some fun wiggles in light areas.

#dithering #riemersmadithering #stippling #halftoneart #raster #pixelart #hilbertcurve #peanocurve #planefillingcurve #spacefillingcurve #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

The previous demo made me dig deeper into dithering algorithms. It's something I should have done years ago, as I've been using simple random dithering now and then, and I hadn't even thought of gamma correction. One algorithm in particular caught my eye: Riemersma dithering, which uses the Hilbert curve. Compared to the usual matrices for error diffusion, the curve approach seemed easier to implement in some ways, as it has fewer edge issues.

More interestingly, it struck a chord with my earlier experiments with space-filling curves in image processing. So it was a kind of familiar territory, but it also seemed esoteric enough that I could imagine making some new discoveries. For example, play with other plane-filling curves besides the Hilbert.

The first image uses the boustrophedon curve, which makes the vertical wave patterns I recall from a number of non-dithering demos. The second curve is what I call the diagstrophedon, a diagonal zig-zag starting from the top left corner, and I think its wavy artefacts make a nice match for Venus's hair.

Then in image 3 we have Hilbert, which doesn't seem to make any particular artefacts, and I guess that's a good thing for dithering. Finally 4 uses the Peano curve, which makes some fun wiggles in light areas.

#dithering #riemersmadithering #stippling #halftoneart #raster #pixelart #hilbertcurve #peanocurve #planefillingcurve #spacefillingcurve #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

The previous demo made me dig deeper into dithering algorithms. It's something I should have done years ago, as I've been using simple random dithering now and then, and I hadn't even thought of gamma correction. One algorithm in particular caught my eye: Riemersma dithering, which uses the Hilbert curve. Compared to the usual matrices for error diffusion, the curve approach seemed easier to implement in some ways, as it has fewer edge issues.

More interestingly, it struck a chord with my earlier experiments with space-filling curves in image processing. So it was a kind of familiar territory, but it also seemed esoteric enough that I could imagine making some new discoveries. For example, play with other plane-filling curves besides the Hilbert.

The first image uses the boustrophedon curve, which makes the vertical wave patterns I recall from a number of non-dithering demos. The second curve is what I call the diagstrophedon, a diagonal zig-zag starting from the top left corner, and I think its wavy artefacts make a nice match for Venus's hair.

Then in image 3 we have Hilbert, which doesn't seem to make any particular artefacts, and I guess that's a good thing for dithering. Finally 4 uses the Peano curve, which makes some fun wiggles in light areas.

#dithering #riemersmadithering #stippling #halftoneart #raster #pixelart #hilbertcurve #peanocurve #planefillingcurve #spacefillingcurve #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

The previous demo made me dig deeper into dithering algorithms. It's something I should have done years ago, as I've been using simple random dithering now and then, and I hadn't even thought of gamma correction. One algorithm in particular caught my eye: Riemersma dithering, which uses the Hilbert curve. Compared to the usual matrices for error diffusion, the curve approach seemed easier to implement in some ways, as it has fewer edge issues.

More interestingly, it struck a chord with my earlier experiments with space-filling curves in image processing. So it was a kind of familiar territory, but it also seemed esoteric enough that I could imagine making some new discoveries. For example, play with other plane-filling curves besides the Hilbert.

The first image uses the boustrophedon curve, which makes the vertical wave patterns I recall from a number of non-dithering demos. The second curve is what I call the diagstrophedon, a diagonal zig-zag starting from the top left corner, and I think its wavy artefacts make a nice match for Venus's hair.

Then in image 3 we have Hilbert, which doesn't seem to make any particular artefacts, and I guess that's a good thing for dithering. Finally 4 uses the Peano curve, which makes some fun wiggles in light areas.

#dithering #riemersmadithering #stippling #halftoneart #raster #pixelart #hilbertcurve #peanocurve #planefillingcurve #spacefillingcurve #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

The previous demo made me dig deeper into dithering algorithms. It's something I should have done years ago, as I've been using simple random dithering now and then, and I hadn't even thought of gamma correction. One algorithm in particular caught my eye: Riemersma dithering, which uses the Hilbert curve. Compared to the usual matrices for error diffusion, the curve approach seemed easier to implement in some ways, as it has fewer edge issues.

More interestingly, it struck a chord with my earlier experiments with space-filling curves in image processing. So it was a kind of familiar territory, but it also seemed esoteric enough that I could imagine making some new discoveries. For example, play with other plane-filling curves besides the Hilbert.

The first image uses the boustrophedon curve, which makes the vertical wave patterns I recall from a number of non-dithering demos. The second curve is what I call the diagstrophedon, a diagonal zig-zag starting from the top left corner, and I think its wavy artefacts make a nice match for Venus's hair.

Then in image 3 we have Hilbert, which doesn't seem to make any particular artefacts, and I guess that's a good thing for dithering. Finally 4 uses the Peano curve, which makes some fun wiggles in light areas.

#dithering #riemersmadithering #stippling #halftoneart #raster #pixelart #hilbertcurve #peanocurve #planefillingcurve #spacefillingcurve #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati