sacred geometry apps

AI generated geometry – revisited a few months later

Sunday, 31 December 2023 by Bruce Rawles

Since 2023 was a breakthrough year for AI, it will be interesting to follow how Artificial Intelligence tools will help geometers with a wide variety of interests leverage this mushrooming technology. I made a few preliminary “mixed bag” tests earlier this year with Dall-E 2. Here are a few more recent AI-generated geometric examples by others.

I was prepared to search for additional examples when I “switched gears” and thought I’d ask my friend and fellow geometer Dave Van Dyke if we could collaborate on some experiments with Dall-E 3 (since he has been using it a lot more than I have lately with fun and impressive results) and here’s what he generated (in less than an hour on a screen-sharing Zoom call) as we thought of prompts together that might provide interesting results; thanks, Dave! Note that Dall-E 3 still doesn’t quite know exactly how to make a precise (regular polyhedron) dodecahedron and other artistic liberties are taken, but still the results seem far more impressive than my more primitive results a few months ago. Here are some of the text prompts used to generate 4 sets of images at a time, some with “more strict” and some with “more creative” parameters selected:

make an image of (a) sea of mirrored geodesic spheres
or
make an image of (a) sea of mirrored dodecahedra

make an image of a translucent dodecahedron filled with multi-colored toroidal rings

make an image of a translucent toroidal ring filled with multi-colored platonic solids

make an image of a large translucent dodecahedron filled with multi-colored jellyfish

make an image of (a) sea of mirrored geodesic spheres with a large multi-colored Sri Yantra in the sky instead of clouds (evidently the reference to the prior image wasn’t used and instead the image was drawn from ideas more akin to mythical/fantasy/religious iconography/ideas)

GeometryCode.com Annual Survey (December 2023)

Friday, 1 December 2023 by Bruce Rawles

Thanks to all of you for your continued and ongoing support of this labor of love website!

It has been quite a while since we’ve had a reader survey or poll! Here are the results of the last one from a couple of decades ago:

Here’s an opportunity to share your geometric interests, passions, curiosities, favorite topics, and whatever you think will be helpful, useful, and fun!

We’ll replicate this survey each year, provide results annually, and hopefully guide our content to where you find existing and unexplored subjects!

Step 1 of 2

I am interested in *

	Hardly (or not at all)	A little	Somewhat	A lot	VERY much
sacred, mystical or symbolic geometry	Hardly (or not at all)sacred, mystical or symbolic geometry Hardly (or not at all)	A littlesacred, mystical or symbolic geometry A little	Somewhatsacred, mystical or symbolic geometry Somewhat	A lotsacred, mystical or symbolic geometry A lot	VERY muchsacred, mystical or symbolic geometry VERY much
books on sacred geometry & related topics	Hardly (or not at all)books on sacred geometry & related topics Hardly (or not at all)	A littlebooks on sacred geometry & related topics A little	Somewhatbooks on sacred geometry & related topics Somewhat	A lotbooks on sacred geometry & related topics A lot	VERY muchbooks on sacred geometry & related topics VERY much
geometric art, graphics, jewelry, decor	Hardly (or not at all)geometric art, graphics, jewelry, decor Hardly (or not at all)	A littlegeometric art, graphics, jewelry, decor A little	Somewhatgeometric art, graphics, jewelry, decor Somewhat	A lotgeometric art, graphics, jewelry, decor A lot	VERY muchgeometric art, graphics, jewelry, decor VERY much
geometric apparel, printed items, wares	Hardly (or not at all)geometric apparel, printed items, wares Hardly (or not at all)	A littlegeometric apparel, printed items, wares A little	Somewhatgeometric apparel, printed items, wares Somewhat	A lotgeometric apparel, printed items, wares A lot	VERY muchgeometric apparel, printed items, wares VERY much
geometric tools, toys, products	Hardly (or not at all)geometric tools, toys, products Hardly (or not at all)	A littlegeometric tools, toys, products A little	Somewhatgeometric tools, toys, products Somewhat	A lotgeometric tools, toys, products A lot	VERY muchgeometric tools, toys, products VERY much
geometric software, applications, links	Hardly (or not at all)geometric software, applications, links Hardly (or not at all)	A littlegeometric software, applications, links A little	Somewhatgeometric software, applications, links Somewhat	A lotgeometric software, applications, links A lot	VERY muchgeometric software, applications, links VERY much
geometric videos and animation	Hardly (or not at all)geometric videos and animation Hardly (or not at all)	A littlegeometric videos and animation A little	Somewhatgeometric videos and animation Somewhat	A lotgeometric videos and animation A lot	VERY muchgeometric videos and animation VERY much
geometry interviews, conversations	Hardly (or not at all)geometry interviews, conversations Hardly (or not at all)	A littlegeometry interviews, conversations A little	Somewhatgeometry interviews, conversations Somewhat	A lotgeometry interviews, conversations A lot	VERY muchgeometry interviews, conversations VERY much
geometry in the natural world, biology, mineralogy	Hardly (or not at all)geometry in the natural world, biology, mineralogy Hardly (or not at all)	A littlegeometry in the natural world, biology, mineralogy A little	Somewhatgeometry in the natural world, biology, mineralogy Somewhat	A lotgeometry in the natural world, biology, mineralogy A lot	VERY muchgeometry in the natural world, biology, mineralogy VERY much
geometry in man-made world, architecture, technology	Hardly (or not at all)geometry in man-made world, architecture, technology Hardly (or not at all)	A littlegeometry in man-made world, architecture, technology A little	Somewhatgeometry in man-made world, architecture, technology Somewhat	A lotgeometry in man-made world, architecture, technology A lot	VERY muchgeometry in man-made world, architecture, technology VERY much
interconnectedness & related topics	Hardly (or not at all)interconnectedness & related topics Hardly (or not at all)	A littleinterconnectedness & related topics A little	Somewhatinterconnectedness & related topics Somewhat	A lotinterconnectedness & related topics A lot	VERY muchinterconnectedness & related topics VERY much
proportions, numbers (e.g. golden ratio, Fibonacci Series)	Hardly (or not at all)proportions, numbers (e.g. golden ratio, Fibonacci Series) Hardly (or not at all)	A littleproportions, numbers (e.g. golden ratio, Fibonacci Series) A little	Somewhatproportions, numbers (e.g. golden ratio, Fibonacci Series) Somewhat	A lotproportions, numbers (e.g. golden ratio, Fibonacci Series) A lot	VERY muchproportions, numbers (e.g. golden ratio, Fibonacci Series) VERY much
fractals, Mandelbrot Set, etc.	Hardly (or not at all)fractals, Mandelbrot Set, etc. Hardly (or not at all)	A littlefractals, Mandelbrot Set, etc. A little	Somewhatfractals, Mandelbrot Set, etc. Somewhat	A lotfractals, Mandelbrot Set, etc. A lot	VERY muchfractals, Mandelbrot Set, etc. VERY much
tilings, tesselations, space-filling geometries	Hardly (or not at all)tilings, tesselations, space-filling geometries Hardly (or not at all)	A littletilings, tesselations, space-filling geometries A little	Somewhattilings, tesselations, space-filling geometries Somewhat	A lottilings, tesselations, space-filling geometries A lot	VERY muchtilings, tesselations, space-filling geometries VERY much
hyperdimensional geometries	Hardly (or not at all)hyperdimensional geometries Hardly (or not at all)	A littlehyperdimensional geometries A little	Somewhathyperdimensional geometries Somewhat	A lothyperdimensional geometries A lot	VERY muchhyperdimensional geometries VERY much
physics, quantum theory, metaphysics	Hardly (or not at all)physics, quantum theory, metaphysics Hardly (or not at all)	A littlephysics, quantum theory, metaphysics A little	Somewhatphysics, quantum theory, metaphysics Somewhat	A lotphysics, quantum theory, metaphysics A lot	VERY muchphysics, quantum theory, metaphysics VERY much
macrocosmic geometry (e.g. planets, galaxies)	Hardly (or not at all)macrocosmic geometry (e.g. planets, galaxies) Hardly (or not at all)	A littlemacrocosmic geometry (e.g. planets, galaxies) A little	Somewhatmacrocosmic geometry (e.g. planets, galaxies) Somewhat	A lotmacrocosmic geometry (e.g. planets, galaxies) A lot	VERY muchmacrocosmic geometry (e.g. planets, galaxies) VERY much
microcosmic geometry (e.g. crystals, molecules)	Hardly (or not at all)microcosmic geometry (e.g. crystals, molecules) Hardly (or not at all)	A littlemicrocosmic geometry (e.g. crystals, molecules) A little	Somewhatmicrocosmic geometry (e.g. crystals, molecules) Somewhat	A lotmicrocosmic geometry (e.g. crystals, molecules) A lot	VERY muchmicrocosmic geometry (e.g. crystals, molecules) VERY much
primal 2D geometric forms (e.g. polygons, curved shapes)	Hardly (or not at all)primal 2D geometric forms (e.g. polygons, curved shapes) Hardly (or not at all)	A littleprimal 2D geometric forms (e.g. polygons, curved shapes) A little	Somewhatprimal 2D geometric forms (e.g. polygons, curved shapes) Somewhat	A lotprimal 2D geometric forms (e.g. polygons, curved shapes) A lot	VERY muchprimal 2D geometric forms (e.g. polygons, curved shapes) VERY much
primal 3D geometric forms (e.g. polyhedrons: Platonic, Archimedean Solids, etc.)	Hardly (or not at all)primal 3D geometric forms (e.g. polyhedrons: Platonic, Archimedean Solids, etc.) Hardly (or not at all)	A littleprimal 3D geometric forms (e.g. polyhedrons: Platonic, Archimedean Solids, etc.) A little	Somewhatprimal 3D geometric forms (e.g. polyhedrons: Platonic, Archimedean Solids, etc.) Somewhat	A lotprimal 3D geometric forms (e.g. polyhedrons: Platonic, Archimedean Solids, etc.) A lot	VERY muchprimal 3D geometric forms (e.g. polyhedrons: Platonic, Archimedean Solids, etc.) VERY much
geometry and sound, music, acoustics	Hardly (or not at all)geometry and sound, music, acoustics Hardly (or not at all)	A littlegeometry and sound, music, acoustics A little	Somewhatgeometry and sound, music, acoustics Somewhat	A lotgeometry and sound, music, acoustics A lot	VERY muchgeometry and sound, music, acoustics VERY much
geometry videos, tutorials	Hardly (or not at all)geometry videos, tutorials Hardly (or not at all)	A littlegeometry videos, tutorials A little	Somewhatgeometry videos, tutorials Somewhat	A lotgeometry videos, tutorials A lot	VERY muchgeometry videos, tutorials VERY much
geometric construction techniques and tips	Hardly (or not at all)geometric construction techniques and tips Hardly (or not at all)	A littlegeometric construction techniques and tips A little	Somewhatgeometric construction techniques and tips Somewhat	A lotgeometric construction techniques and tips A lot	VERY muchgeometric construction techniques and tips VERY much
other geometric topics (please specify)	Hardly (or not at all)other geometric topics (please specify) Hardly (or not at all)	A littleother geometric topics (please specify) A little	Somewhatother geometric topics (please specify) Somewhat	A lotother geometric topics (please specify) A lot	VERY muchother geometric topics (please specify) VERY much

Other geometric or related topics of interest

Digital dabbling with Dall-E

Wednesday, 29 March 2023 by Bruce Rawles

After several years of mixed results with Siri (on my iPhone and MacBook Pro) and cylindrical kitchen add-on Alexa, often amusing and sometimes rather useful, I think my current favorite “Jetson” technology still might be our humble shorter cybernetic cylinder, “Rosie” the Roomba – our household vacuuming robot weekly whisking an amazing amount of fur from feline friends in our home.

Out of curiosity, I recently have done some very preliminary explorations with 2 OpenAI artificial intelligence apps; ChatGPT – rather impressive for certain well-defined tasks – and Dall-E 2. Since the latter seems appropriate for the visual nature of geometric imagery, I gave it a few prompts and got the results below within a span of about 45 minutes. Most of that time was spent thinking up a geometric ideas and then reviewing (clicking on the smaller thumbnails to see the zoomed-in) results; the actual time that the application took to generate the images with about 10-20 seconds for each batch of 4 rendered thumbnails! At its present maturity, Dall-E seems to have some limited usefulness if mathematical precision is less important than artistic conceptual prototypes. What do you think? Fun to play with, of course! The text I typed is followed by the output for each experiment:

experiment 1:
golden glowing dodecahedron hovering above a shimmering sea of 144 smaller iridescent silvery icosahedra

experiment 2:
a fleet of 12 toroidal UFOs arranged in a circle beaming light to the apex of the Great Pyramid of Giza, Egypt with a rainbow gradient sky

experiment 3:
Mandelbrot set made of cedar sprigs in the style of M.C. Escher

experiment 4:
(Anthony James mirrored icosahedron variations by Dall-E; I used this image as input)

experiment 5:
Impressionist painting in the style of Vincent Van Gogh of CERN hardware

experiment 6:
A photo of the Eiffel Tower scaled to fit in the middle of Stonehenge with glowing orbs atop each megalith in the style of Salvador Dali

… with 4 more variations requested:

experiment 7:
7 purple Flower of Life disks wrapped around a silver cone reflected in a parabolic mirror by Rene Magritte (and 2 more sets of 4 variations)

experiment 8:
a photorealistic image of Dorothy from the Wizard of Oz holding hands with Alice in Wonderland standing in front of the Great Pyramid at Giza, Egypt.
(If you look closely at the faces, they look rather wonky at best, but zoomed out not too bad… Of course the 2nd, 3rd and 4th images used the 2nd “Kephren” pyramid which still has the capstone casing and not the Great Pyramid, but this is a learning technology, right. I wonder if the next time someone asks for a similar image, Dall-E will incorporate my comments and stick to just the Great Pyramid?)

TurboSquid 3D geometric models

Tuesday, 31 May 2022 by Bruce Rawles

Fellow geometer, 3D animator, techno-nerd, mystic, and life-long friend, Dave Van Dyke alerted me to some examples of very cool 3-dimensional models using TurboSquid (3D Models for Professionals) a couple of days ago. The links below connect with a small set of the many examples of 3-d geometric models – some free, others inexpensive – all gems, especially considering the “labor of love” efforts put into these detailed models! Going beyond geometric constraints, you have orders of magnitude more to explore! They can be downloaded and adapted wherever your imagination might lead! Here are some samples to pique your interest!

polyhedron made of inter-locking blue squares

geodesic polyhedra (truncated icosahedra); small and large sizes connected at vertices

polyhedron made of interlocking blue triangles — polyhedron made of inter-locking blue triangles

icosa-dodeca-geometric model with wavy extruded interconnecting struts

3-D Polyhedra Software: Modeling, Art, Animation, Apps and more

Monday, 28 September 2020 by Bruce Rawles

If you want to experiment with 3D geometry software, check out Stella from Software3D; lots of possibilities here including the nets (a.k.a. fold-up patterns) for making polyhedra cut out from flat material, such as paper, cardboard or whatever. The animations showing the flattened 2-dimensional nets morphing into their completed 3-dimensional counterparts are particularly fun and useful since you can see intuitively how these polygons all work together to make a whole greater than the sum of its parts. :-)

Among the many other helpful and interesting products and items on this site is the “Worlds Kaleid!” live camera kaleidoscope app for Android.