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  1. "Was man nicht im Kopf hat, muss man im Computer haben" sagt die Collage der nerdigen Nachbarn unter mir. Unabhängig von der Willkür eines US Oligarchen, füge ich hinzu. #DigitalIndipendenceDay #diday #computerart

  2. "Was man nicht im Kopf hat, muss man im Computer haben" sagt die Collage der nerdigen Nachbarn unter mir. Unabhängig von der Willkür eines US Oligarchen, füge ich hinzu. #DigitalIndipendenceDay #diday #computerart

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. VALIE EXPORT, “Räume”, 1991, digital collage #VALIEEXPORT #collage #computerart #cyberfeminism #deconstruction #darkculture #artstars #1990s

    ▝ G ▞ R ▘ E ▞ A ▚ T ▖
    ▚ V ▝ A ▚ L ▖ I ▘ E ▘
    ▘ E ▞ X ▗ P ▚ O ▚ R ▝ T ▖

    iii/xv

  9. Years ago, 2021, I was playing around with @drawBot These are vectors that can not be divided into smaller fractions, like primes. It made an interesting image, fine. Then recently I look for something else in The Computer in Art, Jasia Reichardt from 1971. It shows work of M. R. Schroeder. It is *almost* identical! I had no idea. Some small differences, curious why, but generally: math is universal and will be discovered over and over. #math #computerart #primes #mathematics

  10. Years ago, 2021, I was playing around with @drawBot These are vectors that can not be divided into smaller fractions, like primes. It made an interesting image, fine. Then recently I look for something else in The Computer in Art, Jasia Reichardt from 1971. It shows work of M. R. Schroeder. It is *almost* identical! I had no idea. Some small differences, curious why, but generally: math is universal and will be discovered over and over. #math #computerart #primes #mathematics

  11. Years ago, 2021, I was playing around with @drawBot These are vectors that can not be divided into smaller fractions, like primes. It made an interesting image, fine. Then recently I look for something else in The Computer in Art, Jasia Reichardt from 1971. It shows work of M. R. Schroeder. It is *almost* identical! I had no idea. Some small differences, curious why, but generally: math is universal and will be discovered over and over. #math #computerart #primes #mathematics

  12. Years ago, 2021, I was playing around with @drawBot These are vectors that can not be divided into smaller fractions, like primes. It made an interesting image, fine. Then recently I look for something else in The Computer in Art, Jasia Reichardt from 1971. It shows work of M. R. Schroeder. It is *almost* identical! I had no idea. Some small differences, curious why, but generally: math is universal and will be discovered over and over. #math #computerart #primes #mathematics

  13. Thinking about traditional moorish art, and the distinction between "geometric pattern" versus "algorithmic pattern". These visual designs are geometric. But definitely not algorithmic: humans make these by heuristically matching/filling the pattern, not by rule-following. In computer art we often conflate the two, since most programs to make these would proceed algorithmically. #computerart #MoorishArchitecture

  14. Thinking about traditional moorish art, and the distinction between "geometric pattern" versus "algorithmic pattern". These visual designs are geometric. But definitely not algorithmic: humans make these by heuristically matching/filling the pattern, not by rule-following. In computer art we often conflate the two, since most programs to make these would proceed algorithmically. #computerart #MoorishArchitecture

  15. Thinking about traditional moorish art, and the distinction between "geometric pattern" versus "algorithmic pattern". These visual designs are geometric. But definitely not algorithmic: humans make these by heuristically matching/filling the pattern, not by rule-following. In computer art we often conflate the two, since most programs to make these would proceed algorithmically. #computerart #MoorishArchitecture

  16. Thinking about traditional moorish art, and the distinction between "geometric pattern" versus "algorithmic pattern". These visual designs are geometric. But definitely not algorithmic: humans make these by heuristically matching/filling the pattern, not by rule-following. In computer art we often conflate the two, since most programs to make these would proceed algorithmically. #computerart #MoorishArchitecture

  17. Austin art friends - I am showing one my earliest fractal art pieces in the Bee Cave Arts Foundation's Members Show, beginning next Saturday, May 9 in the Bee Cave Gallaria (same weekend as the Pecan Street Fair). The show is located in the BCAF space, The Hive, across from H&M and Dillards. Hope to see you there!

  18. Austin art friends - I am showing one my earliest fractal art pieces in the Bee Cave Arts Foundation's Members Show, beginning next Saturday, May 9 in the Bee Cave Gallaria (same weekend as the Pecan Street Fair). The show is located in the BCAF space, The Hive, across from H&M and Dillards. Hope to see you there! #abstractart #digitialart #computerart #art #beecavearts

  19. Austin art friends - I am showing one my earliest fractal art pieces in the Bee Cave Arts Foundation's Members Show, beginning next Saturday, May 9 in the Bee Cave Gallaria (same weekend as the Pecan Street Fair). The show is located in the BCAF space, The Hive, across from H&M and Dillards. Hope to see you there! #abstractart #digitialart #computerart #art #beecavearts

  20. Austin art friends - I am showing one my earliest fractal art pieces in the Bee Cave Arts Foundation's Members Show, beginning next Saturday, May 9 in the Bee Cave Gallaria (same weekend as the Pecan Street Fair). The show is located in the BCAF space, The Hive, across from H&M and Dillards. Hope to see you there! #abstractart #digitialart #computerart #art #beecavearts