#algorist — Public Fediverse posts

Metallic Seahorse. 2.5x3.5in ATC format card, metallic green Gelly roll pen on black cardstock. Turing pattern generated using Physarum Type Tool by Maxense Duterne. #penplotter #algorist #1penup #atc #aceo

Metallic Seahorse. 2.5x3.5in ATC format card, metallic green Gelly roll pen on black cardstock. Turing pattern generated using Physarum Type Tool by Maxense Duterne. #penplotter #algorist #1penup #atc #aceo

Metallic Seahorse. 2.5x3.5in ATC format card, metallic green Gelly roll pen on black cardstock. Turing pattern generated using Physarum Type Tool by Maxense Duterne. #penplotter #algorist #1penup #atc #aceo

Metallic Seahorse. 2.5x3.5in ATC format card, metallic green Gelly roll pen on black cardstock. Turing pattern generated using Physarum Type Tool by Maxense Duterne. #penplotter #algorist #1penup #atc #aceo

Two curves, two horses. Turing pattern implementation using Physarum Type Tool by Maxense Duterne.
Each horse is a single line looped plot. B5 size, using Colorverse KSLV-II ink. #penplotter #algorist #plotterart

Two curves, two horses. Turing pattern implementation using Physarum Type Tool by Maxense Duterne.
Each horse is a single line looped plot. B5 size, using Colorverse KSLV-II ink. #penplotter #algorist #plotterart

Two curves, two horses. Turing pattern implementation using Physarum Type Tool by Maxense Duterne.
Each horse is a single line looped plot. B5 size, using Colorverse KSLV-II ink. #penplotter #algorist #plotterart

Two curves, two horses. Turing pattern implementation using Physarum Type Tool by Maxense Duterne.
Each horse is a single line looped plot. B5 size, using Colorverse KSLV-II ink. #penplotter #algorist #plotterart

Uploaded a new SVG https://plotterfiles.com/artwork/hatched-horned-owl-3cpfq
#penplotter #algorist

Uploaded a new SVG https://plotterfiles.com/artwork/hatched-horned-owl-3cpfq
#penplotter #algorist

I haven't made a plotted trading card in a while. Monstera leaf. 2.5x3.5inches, metallic gel pen on brown card stock. #penplotter
#aceo #atc #algorist #plotterart

I haven't made a plotted trading card in a while. Monstera leaf. 2.5x3.5inches, metallic gel pen on brown card stock. #penplotter
#aceo #atc #algorist #plotterart

Peregrine Hawk. A B5 sized plot using Colorverse KSLV-II ink. #penplotter #algorist #animal #bird #hawk

Peregrine Hawk. A B5 sized plot using Colorverse KSLV-II ink. #penplotter #algorist #animal #bird #hawk

Peregrine Hawk. A B5 sized plot using Colorverse KSLV-II ink. #penplotter #algorist #animal #bird #hawk

Peregrine Hawk. A B5 sized plot using Colorverse KSLV-II ink. #penplotter #algorist #animal #bird #hawk

Uploaded a new SVG to plotterfiles.com - Swallowtail Butterfly 1 https://plotterfiles.com/artwork/swallowtail-butterfly-1-81tyz #penplotter #svg #algorist #1penup

Uploaded a new SVG to plotterfiles.com - Swallowtail Butterfly 1 https://plotterfiles.com/artwork/swallowtail-butterfly-1-81tyz #penplotter #svg #algorist #1penup

Gold Star 1. A melding of the parallel line esthetic popular with penplotter artists and Turin pattern.
A single line plot, 100x150mm, gold on black. #penplotter #algorist #1penup #turingpattern

Gold Star 1. A melding of the parallel line esthetic popular with penplotter artists and Turin pattern.
A single line plot, 100x150mm, gold on black. #penplotter #algorist #1penup #turingpattern

Being able to work with or without fills is a key aspect of working with tuned Turing patterns.
The art stands on either plotter or printer. #algorist #reactiondiffusion #penplotter #printer

Being able to work with or without fills is a key aspect of working with tuned Turing patterns.
The art stands on either plotter or printer. #algorist #reactiondiffusion #penplotter #printer

Nested Turing - a pattern in a pattern. SVG available at https://plotterfiles.com/artwork/nested-turing-od574 #penplotter #algorist

Nested Turing - a pattern in a pattern. SVG available at https://plotterfiles.com/artwork/nested-turing-od574 #penplotter #algorist

I'm pretty happy about this one. Green Seahorse. 100x150mm, single loop plot using metallic green Gelly Roll pen on black cardstock.
#penplotter #algorist #plotterart #animalseries #1penup

I'm pretty happy about this one. Green Seahorse. 100x150mm, single loop plot using metallic green Gelly Roll pen on black cardstock.
#penplotter #algorist #plotterart #animalseries #1penup

I'm pretty happy about this one. Green Seahorse. 100x150mm, single loop plot using metallic green Gelly Roll pen on black cardstock.
#penplotter #algorist #plotterart #animalseries #1penup

I'm pretty happy about this one. Green Seahorse. 100x150mm, single loop plot using metallic green Gelly Roll pen on black cardstock.
#penplotter #algorist #plotterart #animalseries #1penup

New SVG uploaded to PlotterFiles. https://plotterfiles.com/artwork/mohawk-7of6r #penplotter #plotterart #algorist #1penup

New SVG uploaded to PlotterFiles. https://plotterfiles.com/artwork/mohawk-7of6r #penplotter #plotterart #algorist #1penup

Time lapse of "Glare", 100x150mm plot white ink on black cardstock. On Youtube #youtube #timelapse #penplotter #algorist https://youtube.com/shorts/HN0JP30_1mA?feature=share

Time lapse of "Glare", 100x150mm plot white ink on black cardstock. On Youtube #youtube #timelapse #penplotter #algorist https://youtube.com/shorts/HN0JP30_1mA?feature=share

Portuguese Ibex. A B5-sized plot, using Colorverse KSLV-II ink. #extinct #penplotter #algorist #animalseries #plotterart

Portuguese Ibex. A B5-sized plot, using Colorverse KSLV-II ink. #extinct #penplotter #algorist #animalseries #plotterart

YouTube Short - time lapse making of "Aguila y Serpiente", plotted on the AxiDraw. #penplotter #youtube #timelapse #algorist https://youtube.com/shorts/CW3wgdAZa_k?feature=share

YouTube Short - time lapse making of "Aguila y Serpiente", plotted on the AxiDraw. #penplotter #youtube #timelapse #algorist https://youtube.com/shorts/CW3wgdAZa_k?feature=share

"Howl" A single loop plot on B5 paper using Colorverse KSLV-II ink. #animal #wolf #penplotter #algorist #onepenup #singleloop
Topologically, it's a circle.

"Howl" A single loop plot on B5 paper using Colorverse KSLV-II ink. #animal #wolf #penplotter #algorist #onepenup #singleloop
Topologically, it's a circle.

"Perched Hawk" A B5-sized plot. Single loop art using Ecoline 337 red ink. One line in a loop. #penplotter #onepenup #algorist #plotterart #animalseries

"Perched Hawk" A B5-sized plot. Single loop art using Ecoline 337 red ink. One line in a loop. #penplotter #onepenup #algorist #plotterart #animalseries

In the last post I introduced the "dual complement" idea for polyhedral graphs. I'm not sure if it has any mathematical significance, but I've made a fun discovery: the dual complement of a spanning tree is another spanning tree.

This result is rather intuitive and I don't have a rigorous proof for it yet, but here are the main supporting ideas. First, a spanning tree over v1 vertices has v1 - 1 edges. We can then show, using basic duality relations and Euler's polyhedral formula, that the dual complement has v2 - 1 edges that connect all of its v2 vertices. The complement doesn't have any cycles, since those would "capture" parts of the original graph, which we know is a single component.

The original polyhedron here is a {3,5+}_2,1 geodesic, so the dual is a Goldberg polyhedron.

No AI, no apps, just my original Python + OpenGL code.

#graphtheory #dualpolyhedron #dualcomplement #spanningtree #geodesicpolyhedron #goldbergpolyhedron #3dgraphics #digitalsculpture #pythoncode #numpy #opengl #creativecodeart #algorithmicart #algorist #mathart #laskutaide #computerart #ittaide #kuavataide #iterati

"Safety Vault" In parkour, the most common maneuver to get over an object. A B5 sized plot #penplotter #algorist #plotterart

"Safety Vault" In parkour, the most common maneuver to get over an object. A B5 sized plot #penplotter #algorist #plotterart

Back in the day, I made a couple of demos where a Hamiltonian path is carved out on a polyhedron. Looking back, I started to wonder about the shape left around the path, and what it means in terms of graph theory. I call this shape the "dual complement" of the path.

The dual of a polyhedron is essentially the result of turning faces into vertices and vice versa. This is shown in the first clip with a snub dodecahedron and its dual, the pentagonal hexecontahedron; to keep the view cleaner, I'm only showing the edges of one at a time.

The duality transformation also affects the edges, but their number remains the same, and there's a 1:1 mapping between the original and dual edges. Each dual edge "cuts through" the original. To make the dual complement of a path, I remove the dual counterpart of each edge in the path, leaving only the stuff on the sides. It's like driving a snow plough along the path, leaving walls of snow on the sides.

For the final view, I combine original Hamiltonian paths with their dual complements.

#graphtheory #hamiltonianpath #hamiltoniancycle #dualpolyhedron #dualcomplement #snubdodecahedron #pentagonalhexecontahedron #3dgraphics #digitalsculpture #pythoncode #numpy #opengl #creativecodeart #algorithmicart #algorist #mathart #laskutaide #computerart #ittaide #kuavataide #iterati

Back in the day, I made a couple of demos where a Hamiltonian path is carved out on a polyhedron. Looking back, I started to wonder about the shape left around the path, and what it means in terms of graph theory. I call this shape the "dual complement" of the path.

The dual of a polyhedron is essentially the result of turning faces into vertices and vice versa. This is shown in the first clip with a snub dodecahedron and its dual, the pentagonal hexecontahedron; to keep the view cleaner, I'm only showing the edges of one at a time.

The duality transformation also affects the edges, but their number remains the same, and there's a 1:1 mapping between the original and dual edges. Each dual edge "cuts through" the original. To make the dual complement of a path, I remove the dual counterpart of each edge in the path, leaving only the stuff on the sides. It's like driving a snow plough along the path, leaving walls of snow on the sides.

For the final view, I combine original Hamiltonian paths with their dual complements.

#graphtheory #hamiltonianpath #hamiltoniancycle #dualpolyhedron #dualcomplement #snubdodecahedron #pentagonalhexecontahedron #3dgraphics #digitalsculpture #pythoncode #numpy #opengl #creativecodeart #algorithmicart #algorist #mathart #laskutaide #computerart #ittaide #kuavataide #iterati

Back in the day, I made a couple of demos where a Hamiltonian path is carved out on a polyhedron. Looking back, I started to wonder about the shape left around the path, and what it means in terms of graph theory. I call this shape the "dual complement" of the path.

The dual of a polyhedron is essentially the result of turning faces into vertices and vice versa. This is shown in the first clip with a snub dodecahedron and its dual, the pentagonal hexecontahedron; to keep the view cleaner, I'm only showing the edges of one at a time.

The duality transformation also affects the edges, but their number remains the same, and there's a 1:1 mapping between the original and dual edges. Each dual edge "cuts through" the original. To make the dual complement of a path, I remove the dual counterpart of each edge in the path, leaving only the stuff on the sides. It's like driving a snow plough along the path, leaving walls of snow on the sides.

For the final view, I combine original Hamiltonian paths with their dual complements.

#graphtheory #hamiltonianpath #hamiltoniancycle #dualpolyhedron #dualcomplement #snubdodecahedron #pentagonalhexecontahedron #3dgraphics #digitalsculpture #pythoncode #numpy #opengl #creativecodeart #algorithmicart #algorist #mathart #laskutaide #computerart #ittaide #kuavataide #iterati

Back in the day, I made a couple of demos where a Hamiltonian path is carved out on a polyhedron. Looking back, I started to wonder about the shape left around the path, and what it means in terms of graph theory. I call this shape the "dual complement" of the path.

The dual of a polyhedron is essentially the result of turning faces into vertices and vice versa. This is shown in the first clip with a snub dodecahedron and its dual, the pentagonal hexecontahedron; to keep the view cleaner, I'm only showing the edges of one at a time.

The duality transformation also affects the edges, but their number remains the same, and there's a 1:1 mapping between the original and dual edges. Each dual edge "cuts through" the original. To make the dual complement of a path, I remove the dual counterpart of each edge in the path, leaving only the stuff on the sides. It's like driving a snow plough along the path, leaving walls of snow on the sides.

For the final view, I combine original Hamiltonian paths with their dual complements.

#graphtheory #hamiltonianpath #hamiltoniancycle #dualpolyhedron #dualcomplement #snubdodecahedron #pentagonalhexecontahedron #3dgraphics #digitalsculpture #pythoncode #numpy #opengl #creativecodeart #algorithmicart #algorist #mathart #laskutaide #computerart #ittaide #kuavataide #iterati

Back in the day, I made a couple of demos where a Hamiltonian path is carved out on a polyhedron. Looking back, I started to wonder about the shape left around the path, and what it means in terms of graph theory. I call this shape the "dual complement" of the path.

The dual of a polyhedron is essentially the result of turning faces into vertices and vice versa. This is shown in the first clip with a snub dodecahedron and its dual, the pentagonal hexecontahedron; to keep the view cleaner, I'm only showing the edges of one at a time.

The duality transformation also affects the edges, but their number remains the same, and there's a 1:1 mapping between the original and dual edges. Each dual edge "cuts through" the original. To make the dual complement of a path, I remove the dual counterpart of each edge in the path, leaving only the stuff on the sides. It's like driving a snow plough along the path, leaving walls of snow on the sides.

For the final view, I combine original Hamiltonian paths with their dual complements.

#graphtheory #hamiltonianpath #hamiltoniancycle #dualpolyhedron #dualcomplement #snubdodecahedron #pentagonalhexecontahedron #3dgraphics #digitalsculpture #pythoncode #numpy #opengl #creativecodeart #algorithmicart #algorist #mathart #laskutaide #computerart #ittaide #kuavataide #iterati

Green Fish. A B5-sized plot using green gel pen ink. This is a single looped line plot. #penplotter #algorist #turingpattern #onepenup #plotterart

Green Fish. A B5-sized plot using green gel pen ink. This is a single looped line plot. #penplotter #algorist #turingpattern #onepenup #plotterart