#creativecodeart — Public Fediverse posts

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

More fun with rhombuses and zonogons

#TilingTuesday #geogebra #animation #loop #MotionGraphics #2d #CreativeCoding #pattern #geometry #CreativeCode #procedural #CreativeCodeArt #design #GraphicDesign #MathArt #zonogon #design #ArtistOnMastodon #ArtistsOnMastodon #graphic #artwork #2D #vector #illustration #illustrator #art #artist #arts #arte #designer #GraphicDesign #MastoArt #FediArt #CreativeToots

Fun with rhombuses and zonogons

#TilingTuesday #geogebra #animation #loop #MotionGraphics #2d #CreativeCoding #pattern #geometry #CreativeCode #procedural #CreativeCodeArt #design #GraphicDesign #MathArt #zonogon #design #ArtistOnMastodon #ArtistsOnMastodon #graphic #artwork #2D #vector #illustration #illustrator #art #artist #arts #arte #designer #GraphicDesign #MastoArt #FediArt #CreativeToots

Some LibreLogo from a few years ago: a modified Pythagorean tree with rainbow colours.

#CreativeCoding #pattern #fractal #Logo #LibreLogo #LibreOffice #TurtleGraphics #geometry #CreativeCode #procedural #CreativeCodeArt #design #2D #GraphicDesign

@scruss The PICTURE command can group objects, and also output SVG animations. Although I’ve made a screen recording here as animated SVGs aren’t accepted

TO CORNER :S
RIGHT 45 FORWARD :S RIGHT 45
END

TO ONESIDE :S :DIAG :LEVEL
IF :LEVEL = 0 [ STOP ]
ONESIDE :S :DIAG :LEVEL - 1
RIGHT 45 FORWARD :DIAG RIGHT 45
ONESIDE :S :DIAG :LEVEL - 1
LEFT 90 FORWARD :S LEFT 90
ONESIDE :S :DIAG :LEVEL - 1
RIGHT 45 FORWARD :DIAG RIGHT 45
ONESIDE :S :DIAG :LEVEL - 1
SLEEP 20
END

TO SIERP :S :LEVEL
:DIAG = :S / 1.414
REPEAT 4 [ ONESIDE :S :DIAG :LEVEL CORNER :DIAG ]
END

CLEARSCREEN
HIDETURTLE
PENUP HOME RIGHT 90 BACK 100 LEFT 90 BACK 100 PENDOWN
; PICTURE "≈" [
; SIERP 10 2
; ]

PICTURE “Sierpinski004.svg” [

repeat 1 [
SIERP 10 4
SLEEP 2000 ]

#animation #SVG #loop #2d #CreativeCoding #pattern #Sierpinski #fractal #Logo #TurtleGraphics #geometry #CreativeCode #procedural #CreativeCodeArt #design #GraphicDesign

@scruss Nice, this version has a few changes to fill the shapes with PENDOWN and PENUP to avoid draw extraneous lines.

TO hx :size
REPEAT 6 [
tri :size FORWARD :size LEFT 60 CLOSE FILL
]
END

TO PT :size
FORWARD :size
RIGHT 150
FORWARD :size
LEFT 30
END

TO superhex :size
REPEAT 6 [
FILLCOLOR "gray" FILLTRANSPARENCY 50 hx :size PU PT :size FORWARD :size LEFT 60 PD
]
END

TO tri :size
REPEAT 3 [
PT :size
]
END

HOME CLEARSCREEN HIDETURTLE
superhex 50

#CreativeCoding #pattern #Sierpinski #fractal #Logo #TurtleGraphics #geometry #CreativeCode #procedural #CreativeCodeArt #design #tiling #GraphicDesign

@scruss Thanks. Here’s the Sierpinski program adapted to run LibreOffice using the built-in LibreLogo environment https://help.libreoffice.org/latest/en-US/text/swriter/librelogo/LibreLogo.html

One of LibreLogo’s advantages is that the output is vector graphics that can be edited (but rasterised here for convenience).

TO CORNER :S
RIGHT 45 FORWARD :S RIGHT 45
END

TO ONESIDE :S :DIAG :LEVEL
IF :LEVEL = 0 [ STOP ]
ONESIDE :S :DIAG :LEVEL - 1
RIGHT 45 FORWARD :DIAG RIGHT 45
ONESIDE :S :DIAG :LEVEL - 1
LEFT 90 FORWARD :S LEFT 90
ONESIDE :S :DIAG :LEVEL - 1
RIGHT 45 FORWARD :DIAG RIGHT 45
ONESIDE :S :DIAG :LEVEL - 1
END

TO SIERP :S :LEVEL
:DIAG = :S / 1.414
REPEAT 4 [ ONESIDE :S :DIAG :LEVEL CORNER :DIAG ]
END

CS
HT
PU HOME RT 90 BK 100 LT 90 BK 100 PD
SIERP 10 4
FILL

#CreativeCoding #pattern #Sierpinski #fractal #Logo #TurtleGraphics #LibreOffice #LibreLogo #geometry #CreativeCode #procedural #CreativeCodeArt

An animation of blue and lilac squares made with Geogebra

#geometry #loop #square #star #IslamicPattern #pattern #CreativeCode #procedural #creativeCodeArt #geogebra #animation #design #MathArt #ArtistOnMastodon #ArtistsOnMastodon #graphic #design #artwork #art #artist #arts #arte #designer #GraphicDesign #MastoArt #FediArt #CreativeToots #MathArt #MathsArt

🫠

#creativecodeart #mastoart

Jitterbug, one of my best-known origami creations.

Geogebra file: https://www.geogebra.org/m/wsxthyaz
Origami instructions: http://foldworks.net/wp-content/uploads/2018/06/jitterbug.pdf

I first came across Buckminster Fuller’s Jitterbug in Amy C. Edmondson’s A Fuller Explanation (1987).

As I didn’t have dowels and four-way rubber connectors, I made several cuboctahedra that worked as Jitterbugs but were not very reversible. Some were from paper and others from drinking straws and elastic thread. This modular origami version is the most recent version.

#geometry #loop #CreativeCode #procedural #creativeCodeArt #geogebra #animation #origami #ModularOrigami #craft #design #PaperCraft #MathArt #ArtistOnMastodon #ArtistsOnMastodon #graphic #design #artwork #3D #art #artist #arts #arte #designer #GraphicDesign #MastoArt #FediArt #CreativeToots #MathArt #MathsArt

High-resolution Render for Patrons of Level Square and up!

10'000 objects moving ~1500 time steps in 25600x14400pixel resolution

#creativecodeart

An experiment using rectangles and circles in #Nodebox 1
#geometry #CreativeCode #procedural #MathArt #CreativeCodeArt #NodeBox #ShoeBot

Hyperbolic Fractal made from truncated cuboctahedra

Full MusicalVersion: https://youtu.be/JSJjuro3-PM

#creativecodeart #fractal #mathart

Subdivision made in #NodeBox 1 inspired by Sol LeWitt
#geometry #loop #creativecode #procedural #MathArt #creativecodeart #genuary #NodeBox #shoebot

Good Morning! 🌅

#creativecodeart

#creativecodeart #automata