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Numbers and Proportions

Fractal and Geometric Animations

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Here are some interesting geometric animations… Lots more to explore!

A few example animations found using sacred geometry as a search term on Giphy:

Fractal (Octahedra) Polyhedra with Sierpiński triangle faces via GIPHY

A Flower of Life variation with animated rainbow colors via GIPHY

Fractal (Dodecahedra) Polyhedra with pentagon faces via GIPHY

A couple of example animations found using polyhedra as a search term on Giphy:

A Rhombic Triacontahedron appears when the animated mesh reaches its finest resolution; here’s a fold-up pattern for the Rhombic Triacontahedron (a.k.a. Kepler’s Solid). Here’s the animation via GIPHY.

Each edge of the triangular faces of this lovely icosahedron is subdivided 4 times. Here’s the animation via GIPHY.

… and a few example animations found using fractal as a search term on Giphy:

Fractal gears via GIPHY

Fractal dogs/ears via GIPHY

Koch snowflake via GIPHY

Whirling squares (golden ratio spiral) animation
whirling-squares-golden-ratio (frame from animation)

Thanks to fellow geometer Dave Van Dyke for pointing these out to me.

A few German sacred geometry books available for shipping costs only

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Update 21 July 2024: We’ve been in Arizona for exactly a year today, and I still have a handful of German books to find homes for, so I’m re-dating this post in case anyone would like to purchase a book for only my shipping costs!

(Originally published 25Jun2023):

We’re making good progress toward moving to Arizona (mid-July 2023)  so I’m anticipating having more time to do in-depth posts after our move. Meanwhile, I’d still like to lighten our load and not move these books yet another time… I’m offering (until mid-July, while supplies last) – limited supply; limited offer) asking only for my shipping costs (US only) or free if you happen to be on the central Oregon coast and can pick them up here in Yachats before we move! in the Tucson, AZ metro area and can pick them up.

German sacred geometry books are available for shipping only (for a limited time!)

I have a handful of both of my German-translated books:

(If you live in Germany, you’ll probably want to order the Bewusst malen – Heilige Geometrie book, still in print, directly from the publisher, Silberschnur Verlag, since the shipping from the USA to Germany is likely more than buying it locally.)

If you speak German or know someone who does and has the least interest in geometry, I am offering special FREE books (very limited supply) of both of these books if you cover my postage costs. If you live near Yachats, Oregon, Green Valley, Arizona, you can pick them up here and skip the postage expense. For details on these limited-time, limited-supply books, contact me.

Note that you don’t have to be able to read or understand German to enjoy either of these books, as they are both lavishly illustrated – FAR more imagery than text. Also, each copy of the out-of-print MDHG book has a unique set of die-cut fold-up models of the 5 Platonic Solids (included behind the back cover) that make a neat mobile if you add your own thread.

MDHG Platonic Solid fold-up mobile

Please contact me before mid-July 2023 if you are interested in this special offer!

Mandalas der Heiligen Geometrie (MDHG): German edition of Sacred Geometry Design SourceBook by Bruce Rawles - GeometryCode.com

sacred geometry coloring book (German): Bewusst malen - Heilige Geometrie by Bruce Rawles

Here are a few more interesting geometry-related links (videos) that have crossed my path recently; several short introductory videos that add some useful and interesting additions to commonly cited facts:

  • Golden Spiral Symbol – What Does It Mean?
  • What Makes the Golden Spiral Symbol Special?
  • What is Sacred Geometry? (evidently using an AI-generated voice/script?)
  • How Does the Golden Spiral Relate to Sacred Geometry?
  • What is the Meaning of the Golden Spiral?
  • What are Some Examples of the Golden Spiral?
  • What is the Fibonacci Sequence?
  • … and several others…

AI generated geometry – revisited a few months later

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

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

Dall-E 3 AI-generated image using prompt "make an image of a translucent toroidal ring filled with multi-colored platonic solids" thanks to Dave Van Dyke Dall-E 3 AI-generated image using prompt "make an image of a translucent toroidal ring filled with multi-colored platonic solids" thanks to Dave Van Dyke Dall-E 3 AI-generated image using prompt "make an image of a translucent toroidal ring filled with multi-colored platonic solids" thanks to Dave Van Dyke Dall-E 3 AI-generated image using prompt "make an image of a translucent toroidal ring filled with multi-colored platonic solids" thanks to Dave Van Dyke Dall-E 3 AI-generated image using prompt "make an image of a translucent toroidal ring filled with multi-colored platonic solids" thanks to Dave Van Dyke Dall-E 3 AI-generated image using prompt "make an image of a translucent toroidal ring filled with multi-colored platonic solids" thanks to Dave Van Dyke Dall-E 3 AI-generated image using prompt "make an image of a translucent toroidal ring filled with multi-colored platonic solids" thanks to Dave Van Dyke Dall-E 3 AI-generated image using prompt "make an image of a translucent toroidal ring filled with multi-colored platonic solids" thanks to Dave Van Dyke

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

Dall-E 3 AI-generated image using prompt "make an image of a large translucent dodecahedron filled with multi-colored jellyfish" thanks to Dave Van Dyke Dall-E 3 AI-generated image using prompt "make an image of a large translucent dodecahedron filled with multi-colored jellyfish" thanks to Dave Van Dyke Dall-E 3 AI-generated image using prompt "make an image of a large translucent dodecahedron filled with multi-colored jellyfish" thanks to Dave Van Dyke Dall-E 3 AI-generated image using prompt "make an image of a large translucent dodecahedron filled with multi-colored jellyfish" thanks to Dave Van Dyke

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)

Dall-E 3 AI-generated image using prompt "make an image of (a) sea of mirrored geodesic spheres with a large multi-colored Sri Yantra in the sky instead of clouds" thanks to Dave Van Dyke Dall-E 3 AI-generated image using prompt "make an image of (a) sea of mirrored geodesic spheres with a large multi-colored Sri Yantra in the sky instead of clouds" thanks to Dave Van Dyke Dall-E 3 AI-generated image using prompt "make an image of (a) sea of mirrored geodesic spheres with a large multi-colored Sri Yantra in the sky instead of clouds" thanks to Dave Van Dyke Dall-E 3 AI-generated image using prompt "make an image of (a) sea of mirrored geodesic spheres with a large multi-colored Sri Yantra in the sky instead of clouds" thanks to Dave Van Dyke Dall-E 3 AI-generated image using prompt "make an image of (a) sea of mirrored geodesic spheres with a large multi-colored Sri Yantra in the sky instead of clouds" thanks to Dave Van Dyke Dall-E 3 AI-generated image using prompt "make an image of (a) sea of mirrored geodesic spheres with a large multi-colored Sri Yantra in the sky instead of clouds" thanks to Dave Van Dyke Dall-E 3 AI-generated image using prompt "make an image of (a) sea of mirrored geodesic spheres with a large multi-colored Sri Yantra in the sky instead of clouds" thanks to Dave Van Dyke

Dall-E 3 AI-generated image using prompt "make an image of (a) sea of mirrored geodesic spheres with a large multi-colored Sri Yantra in the sky instead of clouds" thanks to Dave Van Dyke

GeometryCode.com Annual Survey (December 2023)

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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
Hardly (or not at all)A littleSomewhatA lotVERY much
sacred, mystical or symbolic geometry
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books on sacred geometry & related topics
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geometric art, graphics, jewelry, decor
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geometric apparel, printed items, wares
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geometric tools, toys, products
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geometric software, applications, links
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geometric videos and animation
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geometry interviews, conversations
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geometry in the natural world, biology, mineralogy
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geometry in man-made world, architecture, technology
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interconnectedness & related topics
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proportions, numbers (e.g. golden ratio, Fibonacci Series)
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fractals, Mandelbrot Set, etc.
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tilings, tesselations, space-filling geometries
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hyperdimensional geometries
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physics, quantum theory, metaphysics
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macrocosmic geometry (e.g. planets, galaxies)
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microcosmic geometry (e.g. crystals, molecules)
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primal 2D geometric forms (e.g. polygons, curved shapes)
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primal 3D geometric forms (e.g. polyhedrons: Platonic, Archimedean Solids, etc.)
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geometry and sound, music, acoustics
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geometry videos, tutorials
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geometric construction techniques and tips
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other geometric topics (please specify)
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Affiliates and Archives Galore!

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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!