3D Geometries

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

Affiliates and Archives Galore!

Tuesday, 31 October 2023 by Bruce Rawles

I was looking through prior posts – I’ve been sharing items of interest about geometry and interconnectedness since 2007! – and realized that there is a lot of content that is still every bit as relevant today as when originally published … Since geometrical principles, archetypes, and so many more topics aren’t seasonal or slaves to style… at least as far as I can tell! So, I’m going to pull a couple of images with links to older posts to encourage exploration of the archives. Here’s one about Intention and Symbols and when I followed the link about Villarceau circles I found an interesting animation that shows a plane intersecting a torus to reveal a Vesica Piscis cross-section; neat! (I also added the animation to the original post.)

Here’s another post from a while ago:

Dodecahedra Origami Luminaria – a timely holiday project, too!

I just updated our Affiliates page since it’s been quite a while; thanks for many years of support! When you use the links on this page, it helps fund our “labor of love” efforts keeping this site going and this is greatly appreciated!

2024 Martineau Solar System Calendars available now

Saturday, 30 September 2023 by Bruce Rawles

Once again this perennial calendar is available! These timeless images portray amazingly accurate geometric representations of the planetary orbits in our very own solar system – now available in printed calendar form with dates for 2024!!

Martineau Solar System Calendars

These 12 images are highly accurate geometric models of our solar system; details are here. They were inspired by the remarkable work of John Martineau (publisher of Wooden Books), who wrote “A Little Book of Coincidence”. Tiled images of planetary surfaces and related images form the backgrounds. Images are two or more orbits defined by simple 2D (circles, triangles, squares, pentagons, hexagons, octagons) or 3D geometries (e.g. tetrahedron, icosahedron, dodecahedron) typically with 99.9% or greater accuracy. The work picks up where Johannes Kepler’s mystical exploration left off. A newly revised calendar (which is updated every year) with images from the Martineau Solar System is again available for 2024.

Cactus, spirals, and desert geometries

Monday, 31 July 2023 by Bruce Rawles

This will be a short and mostly visual post as we just moved to (Green Valley) Arizona a week or so ago and are getting settled in. Going for early morning walks affords opportunities to observe spiral patterns (and other geometries) in ubiquitous and numerous varieties of cacti. For fun, I’ve added a shot of a vesica piscis shape formed from intertwined trunks, a triangular spiral on a decorative metal screen and there are plenty of obvious geometric patterns as are always evidenced when looking at nature.