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Penrose and other Tilings: periodic and aperiodic – video exploration

Friday, 30 October 2020 by Bruce Rawles

Homage To Kepler's model of the solar system
Kepler’s Model of the Solar System (nested Platonic Solids) and other fun and somewhat boggling geometric explorations unfold in this visually engaging video presentation about periodic … and aperiodic pentagonal tilings discovered by Roger Penrose, quasicrystals, and – of course – cameo appearances by the Golden Ratio and the Fibonacci Series. Enjoy! :-)

Thanks to Shaun L. for alerting me to this gem of a video!

Kepler's solar system models - outer and inner

If you’d like to explore the various periodic tilings and/or Platonic Solids (both mentioned in the video above) and much more, check out my first book, Sacred Geometry Design Sourcebook: Universal Dimensional Patterns!

Sacred Geometry Design Sourcebook - cover

 

Filed Under: 2D Geometries, 3D Geometries, Fibonacci Numbers, Fractal Geometry, Numbers and Proportions, Platonic Solids, sacred geometry animation, sacred geometry art, sacred geometry coloring books, sacred geometry videos

In memoriam: Keith Critchlow

Sunday, 31 May 2020 by Bruce Rawles

Keith Critchlow
Keith Critchlow

I recently learned of the passing of Keith Critchlow through this obituary in The Guardian. One of my first introductions – in the early 1970s – to what has become known as sacred geometry was through the books of Keith Critchlow, notably Order In Space and later, Islamic Patterns: An Analytical and Cosmological Approach. The former book has small illustrations of the tesselations (2-D tiling patterns) comprised of regular polygons. I thought these classic regular tilings all merited a full page (along with numerous archetypical variations) – so these make up a considerable portion of my first book, including pages 16-42, plus other tiling patterns inspired by these on pages 43-95, many unique to SGDS.

Here’s an example (page 27) of one of the small sketches from Prof. Critchlow’s book that I expanded and gave an entire page, in order to facilitate photocopying, coloring – for adults or “kids” of any age, arts, crafts or what have you…

You’ll note that on these 2D tesselation pages I’ve also added “unit cell” variations that show some of the possible groupings of polygon components that can make “step and repeat” (via horizontal and/or vertical translation) patterns that tile the plane in two dimensions.

Sacred Geometry Design Sourcebook example: 4 Triangle, 2 Square Grid (page 27) copyright (c) 1997 Bruce Rawles

I’m not sure if Order In Space was my first exposure to the 5 Platonic Solids and 13 Archimedean Solids, but this may be likely, and pages 196-214 in Sacred Geometry Design Sourcebook – Universal Dimensional Patterns were certainly inspired – in part – by Critchlow’s illustrations. You can find other useful tables in the back of SGDS that were also helped by the example of Critchlow’s generous offerings of useful patterns, ideas, and interconnections.

Elsewhere in Order In Space, he shows a matrix grid chart of the various possible permutations of nesting the 5 Platonic Solids inside each other. Again, these lovely little sketches seemed to merit full-page treatment, so they contributed to pages 224-229 in SGDS.

When I was nearing completion of SGDS in 1997, I sent a review copy to Professor Critchlow, and he sent a very thoughtful reply which included this testimonial:

“A valuable source book of geometric patterning, very useful data, a reminder of the supra human source of such mathematical forms.”

He also provided some very appropriate advice (which certainly aligned with my own experience) in advance of the initial publication, so I added this underlined sentence to page 5 of SGDS paying homage to what must be many millennia of geometers using straightedge and compass for discovery:

“I strongly encourage experimentation and particularly duplication with your own hand.”

Thanks for many years of inspiration, Keith!


Lots more to explore!!! In the process of researching archives online as well as my own prior work to find 2D tilings and tessellations, I found this excellent Wikipedia page: List of regular polytopes and compounds, which expands this topic into many fascinating connected subjects. Here’s a particularly lovely example image from the Hyperbolic star-tilings section:

Filed Under: 2D Geometries, 3D Geometries, Archimedean Solids, Platonic Solids, polyhedra, sacred geometry art, sacred geometry books, sacred geometry coloring books, sacred geometry news Tagged With: Keith Critchlow

The Geometry Code Kindle edition: 6 years ago … Fun geometry videos

Saturday, 29 September 2018 by Bruce Rawles

On Sep. 28, 2012 the Kindle version of my second book, The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation, was launched, a few months after the paperback version. Thanks to one and all for your support this past 6 years and for over two decades since my first book, Sacred Geometry Design Sourcebook (SGDS) – Universal Dimensional Patterns was published! Much appreciated! (SGDS, if you’re new to this realm, is – among other things – a sacred geometry coloring book for adults.) I always enjoy hearing from you … how these have added to your enjoyment of geometric … and more recently metaphysical … explorations or by way of other interconnected conversations!

I recently discovered some fun videos by StandUpMaths that will certainly appeal to the nerdier among us, but are general enough to be fun for a wide range of those even slightly interested in geometry, science, math, etc. I started with “Stand-up comedy routine about Spreadsheets” and then progressed to this fun demo of toroidal vortices “Stand-up comedy about Equations That Correspond to Vortex Motions (aka ‘smoke rings’)”

toroidal vortices: smoke ringsI wonder how long dolphins have been blowing bubble rings? Douglas Adams might have been on the right track suggesting they were smarter than humans. :-)

Here’s a 4D puzzle you might enjoy which helps explain our limited perspective here in this surreal 3D world: Dodecaplex: the puzzle from the fourth dimension! If you’re a hyperdimensional dodecahedra fan, you won’t want to miss this! Enjoy!

Filed Under: 2D Geometries, 3D Geometries, coloring books for adults, sacred geometry art, sacred geometry books, sacred geometry coloring books, sacred geometry physics, sacred geometry videos

Inspirit – Hexagonal kaleidoscope mandala generator iOS app

Saturday, 2 September 2017 by Bruce Rawles

inspirit iOS app - screen snap exampleA new iOS app called Inspirit provides (hexagonal symmetry) kaleidoscopic animation imagery. It appears that there will be options to show either a single hexagon (1 image cropped, reflected and rotated in traditional kaliedoscopic fashion), as well as a fully tiled image (with the hexagonal “cell” translated vertically and horizontally to file a honeycomb (hexagonal) grid. Example video here:

(Thanks to Luke G. for alerting us to this new item.)

Filed Under: 2D Geometries, sacred geometry art, sacred geometry coloring books, sacred geometry videos

Midnight in the Desert – interview July 24, 2017

Sunday, 23 July 2017 by Bruce Rawles

I will be the guest of Midnight In The Desert (MITD) – Late Night Talk Radio with Heather Wade from 9:30PM-1AM on Monday, July 24, 2017. Here is the page on the MITD site about my conversation: – Bruce Rawles – The Ubiquitous Hermetic Laws.

I will be conversing about : Non-dual Metaphysics, Sacred Geometry, The Seven Hermetic Laws, Lessons from Modern Physics, The Great Pyramid of Giza. Please join us! :-)

 

Filed Under: Archimedean Solids, audio, coloring books for adults, Fibonacci Numbers, Fractal Geometry, Hermetic Laws, modern physics, Numbers and Proportions, Platonic Solids, polyhedra, sacred geometry art, sacred geometry books, sacred geometry coloring books, sacred geometry interviews, sacred geometry news

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