Formation of Fibonacci Spirals In Nature

Thanks to Rich in Penn Valley, California for this article:
Scientists find clues to the formation of Fibonacci spirals in nature.

Mission, Vision, Values

I found this bit of musing on a page from my old website, while moving files over to the new one:

I see a world

where the intent of all creation is:
• to deeply feel the love of the Great Spirit, the Creator, and express that love in every thought, word and action, by unfettered choice, with commitment and integrity
• to know, with every atom of one's being, that what appears to be "we" is really "I"; to realize, more profoundly than the mere notion that we are all interconnected, that we ARE indeed cells of an infinite organism and each cell is boundless and precious beyond measure
• to become aware of the glorious unlimited spectrum of life in its inexhaustible beauty, wisdom and diversity, treating all creatures with compassion and respect
• to live in a sustainable way where we cherish the freedom and responsibility to share the truth and care for all aspects of the seamless fabric of life
• to recognize that all appearances of polarity and duality are but illusory reflections of a more profound underlying unity, and grasping the gift of this omni-present mirroring, savor the full range of life's blessings while not taking any thing too seriously
• to find joy and meaning in each moment, purpose in each atom, divine order in every pattern from the most minute to the most unimaginably vast
• to see the Universe through the eyes of gratitude, appreciation and humor.

Unsuggester and SGDS

I guess I need to encourage more folks (73 more, evidently) on the Unsuggester website to fess up to owning (or just order :^) a copy of my book, before it will tell me what I (we mystical geometers) probably won't like... Here's what it spit back to me when I tried it (just out of curiosity and a sense of whimsy)... to see what might be interesting to read as the "opposite library" to get a complete perspective! Happy

Unsuggester takes "people who like this also like that" and turns it on its head. It analyzes the thirteen million books LibraryThing members have recorded as owned or read, and comes back with books least likely to share a library with the book you suggest. The unsuggestions come from LibraryThing data, not from Amazon. LibraryThing also produces great suggestions. (Update 2/24. I just regenerated the recommendations. Some of the examples on the right are no longer the first result. I'll update them soon.)
0965640582.01._SCMZZZZZZZ_UnSuggestions for Sacred Geometry Design Sourcebook: Universal Dimensional Patterns by Bruce Rawles
2 members (690,229 more popular). Members with the book have have a total of 1,879 books in their libraries (see good suggestions).

Sorry. A book must be owned by at least 75 members to have unrecommendations.

Cosmic Rays and Great Pyramid

Here's a recent email from my friend Tim in China who was interested in energy photographs of pyramids, and my response.

I spent a good part of the day looking at several sites, including your blog, hoping to get closer to an understanding of exactly how Sacred Geometry affects us mentally/emotionally/physically. I found an energy photograph taken of a pyramid. The pyramid, based on the Great Pyramid, has energy streaming in a double vortex (like DNA) out the apex. It is clear that something is going on.

The photograph of energy around pyramids I wish I had a copy of was created by a composite of computer data compiled by a former neighbor of mine, Nick Chakakis, who was working for Lawrence Livermore Lab in the early 1970s and had set up an elaborate set of parallel detectors underneath the 2nd pyramid at Giza, Egypt (usually ascribed to Kephren, in much the same way the White House might some day be called the Pelosi House by future archaeologists, I imagine Happy Any way, what Nick showed me before I went to Egypt in the fall of 1973, was a photograph (computer simulation, really) showing the accumulated totals of cosmic ray particles that had passed through the massive thickness of limestone blocks composing the 2nd pyramid. My understanding is that when a high energy cosmic ray particle (mu meson if I recall my college physics correctly?) passed through an X-Y matrix of wires in an evacuated, (inert gas filled?) chamber, it was registered and within a nanosecond, give or take, it would also register with a similar X-Y matrix a meter or so away. Depending on the angle, the number of particles registered varies widely. Measurements were taken over many days to give a "portrait" of the thickness of the stone. They took these measurements from several places far enough apart that they could create a 3D model of the thickness of the stone in order to pinpoint where any hidden chambers might be. Most of their "photos" looked upward, but they "took" one photo looking (through hundreds of feet of solid limestone) toward the Great Pyramid. What was evident in the image was an unmistakable outline of the Great Pyramid on the horizon, which was black (since below the horizon there are vastly fewer cosmic particles that make it through thousands of miles of earth compared with a few hundred feet of stone). However... and this is what impressed me most... there was a distinct "halo" or "corona" around the Great Pyramid with a bright emphasized area around the capstone area. If the pyramid shape was "neutral" there should have just been an abrupt edge with roughly the same intensity for the "sky" area" and fairly uniform intensity for the "Great Pyramid" area. However, this corona seemed to match what I'd just learned from attending a lecture by Patrick Flanagan around that same time, that the shape acts as a lens to focus cosmic energy, and everything in my direct and indirect experience seems to support this.
I also heard somewhere (perhaps Peter Tompkins book?) anecdotally that pilots don't fly directly over the Great Pyramid, because their instrumentation goes wacky... I was able to contact Nick a few years ago, but he wasn't able to find that photo...alas.

Updated page on Martineau Solar System Series & article in journal Symmetry

Another update on the "cattle drive" I'm doing this week : here's an update on my Martineau Solar System Series. I also just received a complimentary copy of Symmetry: Culture and Science, Vol 16, No. 2, 2005, (Journal of the Symmetrion, editor: György Darvas, Polyhedra, Part 3; postal address: Budapest, P. O. Box 994, H-1245 Hungary) which has an article I submitted a few years ago on this subject on pages 193-196. You can also get a calendar with all 12 of these images here, and another with my Homage to Kepler art as a bonus cover image here. Here's an image from one of the first exhibits of this work at South Yuba Club in Nevada City, California.


New Community page and SSI

I'm doing a "cattle drive" this week : moving about 12 years worth of web content from our intent domain (which is going to a new steward on May 1 who plans to do some inspiring things with it!)... so here's a new community page on my newest website (still VERY much a work in progress this week), but you can see some of the little dogies in the new pasture before the rest arrive Happy

BTW, kudos for whoever invented
Server Side Includes (SSI)... this little method of building pages on the fly from the server (and not duplicating a gazillion identical block of HTML!) is already saving me a ton of time! This is why most of the pages on my new site have a .shtml suffix instead of a .html one.

Sonic Wind Sculptures by Ross Barrable

Thanks to Tim A. in China (and North Carolina) for this link with a great quote from Galileo, inspiring text and very interesting (and lovely) sculptures; I'd enjoy hearing the wind through them... I 'resonate' to the text, so I'll post a link to my blog about them... Happy

A couple of minor corrections on that page:

Geometry literally means “the measure of the earth" ... adding 'sacred' just adds the meaning and significance of that word Happy

Also, on that same page, the author/artist refers to the square root of 3 as transcendental. In mathematical terms (to be technically correct), I believe that number is just irrational. However, Pi, (the circumference/diameter proportion of any circle) which is almost always "nearby" or present whenever the square root of three is involved geometrically (either with the vesica piscis made from two circles, or the diagonal of a cube which can be perfectly inscribed or circumscribed by a sphere containing an infinity of circles) IS a transcendental number. In my presentations, I often share the metaphor that an irrational number (like the square roots of 2, 3, or 5) is not resolvable by our conscious 'rational' minds; however a transcendental number (like Pi) is not only irrational, it also transcends this 'dimension', since it can't be expressed even as a polynomial fraction (a fraction made of whole number polynomials, or numbers raised to higher powers or 'dimensions' metaphorically.)

Here's a
link to the MathWorld reference on transcendental numbers. Along with Pi, Euler's number, e (the base of natural logarithms) is perhaps also commonly known to many.

Big Wisdom, Great Music, Short Film

Check out this touching, funny, inspiring and very wise little film online (you can watch it in about a half hour - time well spent!)...

Wombat: We're All One... Interconnected

How perfect for Earth Day ... Thanks to Charley for sending the link to this fun and astute little animation!

Truchet Tiling

For tesselation and tiling fans, here's a page from MathWorld about a tiling that uses diagonals of a square to make some decorative patterns: Truchet Tiling. Here are a few other pages I've contributed to on MathWorld, courtesy of Eric Weisstein.

Foster Gamble & The Fundamental Patterning of the Universe and Us

I checked out an excellent video from RVML: Foster Gamble who spoke on The Fundamental Patterning of the Universe and Us. His fascinating talk links together work of other esteemed colleagues such as Arthur Young, Nassim Haramein, and Walter Russell. The sections describing the unified field implications of the Isotropic Vector Matrix and how the Periodic Table of the Elements relate to geometric models were of particular interest, with many more worthy topics explored. I met Foster briefly in Ashland a few years ago.

Dana Thibault - Fractals: The Language Of Nature

I checked out an excellent video (VHS) from RVML: Dana Thibault - Fractals: The Language Of Nature. This may be the best video I've ever seen on fractals, with some of the simplest explanations for both novice and veteran explorers alike. He also does an excellent job of explaining the fractal nature of some key crop circle formations.

Platonic Solids Info

Thanks to Dan Radin for sending me a link to his website on Platonic Solids which has animations, Origami and more.


For those of you interested in a generalized Fibonacci sequence (summing the prior n terms) here's a reference; thanks to Michael in Arizona.

Yi-Jing Algebra

Thanks to Ed Kellogg for finding this interesting cube / I Ching relationship.

Water-powered Cars

Here's some info about cars that run on water... I'd like to learn more!

Species Alliance

Thanks to Charley for this link to a video about the Species Alliance... our planet needs our support!

Sri Yantra meets Sound of Music meets Lewis Carroll

Thanks to Nancy, Robin & Ed (and probably a few others) for suggesting this film. Last night a couple of friends, my wife & I went to see the movie, The Last Mimzy. I was immediately reminded of the classic Julie Andrews in the Alps panorama (from the Sound of Music) in the breathtaking opening (and closing) scenes. Overall, I'm glad I saw the film, since it did offer the public some interesting glimpses and questions about the importance of following intuition, the relationship of geometry to consciousness, dreams, and energy technology (although I'm waiting for a Hollywood film to show an entire region of a country suddenly and mysteriously powered perfectly by a benign energy source, eliminating the need for non-renewables, rather than the cliché blackout scenario - I guess that will require some clever script-wiring to make that seem dramatic! It almost seems like the mass thinking imposed by a trillion dollar energy industry requires commercial films to portray innovative technologies as disruptive.

The story was fun (although why not lose the 'scary factor'? Perhaps the script writer indulged in our cultural bias toward trembling when the subject of math is raised? Happy I also enjoyed a handful of other geometric references, the Sri Yantra (page 195 of
my book) got the most exposure, although never mentioned by name, not that words are needed for geometric symbols to convey their wisdom! I also enjoyed a cameo appearance of a ZomeTool model... a REAL fun toy I recommend highly! Other animations and graphics showed geodesic, helices, spirals and a handful of other geometric archetypes, mostly for artistic effect, but I guess turning the story into a documentary would have "broken the spell". Some lovely scenery, fun visuals and relatively minimal abuse of important topics that Hollywood rarely touches. I liked the levitation scenes, although I'd like a time travel/futuristic movie to show teleportation (without external technology) as being our natural state as described as one of our natural abilities in the Baird Spalding books. Aside from the minuses already mentioned, some valid concerns on other movie reviews, and some blatant semiconductor and soft drink product placements, I liked the film.

Constance Demby - Luminescent Sonic Immersion

Thanks to friend and author Jodine Turner for providing a link to a lovely 5-minute, visually and musically rich excerpt from Space Music pioneer Constance Demby's Luminescent Sonic Immersion ... The metal rod/sheet (?) instrument evidently called a "Space Bass" looks like it would be great fun to play...

Tesseract Turning Inside Out

Thanks to Alan and folks in the Polytopia Yahoo group (some neat geometric posts!), here's a neat little animation of a Tesseract (Hypercube or 4D Polytope equivalent of a cube) Turning Inside Out

Another example of how our limited 3D body-minds get kinda warped trying to grok our infinite nature (and the various manifestations thereof... Happy

Excerpt from Dan's Interview at Mobius

As part of the First Friday art series, last Friday (see my blog post for 6 April 2007) I was in Ashland, Oregon at the Mobius Gallery showing and answering questions about giclée (and larger) prints of my "Martineau Solar System Geometry" Series which will be on exhibit there through the end of this month.

Many thanks to
Dan Shaw of Vortex Maps who sent me this clip of the video he took of me talking about the art! Greatly appreciated, Dan!!! Happy


Useful Resources for Ecology & Economy

Nancy found this handy reference for local resources (Jackson County, Oregon) for ecology and economy; anything but the landfill, please! You probably have a similar resource online where you live. Favorites you probably already know about are FreeCycle and Craigslist ... there are MANY others that help finding appropriate homes for items no longer needed.

Upper Table Rock - Flowers du jour

A sample of the profusion of little wildflowers blanketing Upper Table Rock (just north of Medford, Oregon) on this morning's hike.


flyer I made for last night's Artists Reception

Here's a flyer I made for last night's Artists Reception at the Mobius Gallery/Venue in Ashland, Oregon, showing: representative samples of my work (from left to right):

Calendars of the Martineau Solar System Series
Geometry Code Screen Saver & Meditation Tool
Sacred Geometry Design Sourcebook


Mobius Art Exhibit & First Friday Event

Tonight (Friday, 6 April 2007) I will be in Ashland, Oregon at the Mobius Gallery from 4:30-9PM showing and answering questions about giclée (and larger) prints of my "Martineau Solar System Geometry" Series which I just finished hanging; thanks to Marla from the Mobius for her assistance! Here's a press release I'm sending out last minute:



Press Release – For Immediate Release
Accurate Geometric Models of Solar System - Art at Mobius Gallery in April & First Friday

The Mobius, 281 4th Street, Ashland, Oregon 97520

When: Exhibit open now through April 30; First Friday artist reception 5-9PM 6 April 2007

What: 12 giclée prints of "The Martineau Series", digital art inspired by breakthrough discoveries about our solar system and how the orbits of the planets relate to simple geometric models.

Who: artist and geometer Bruce Rawles

As part of the
First Friday art series, the Mobius is currently exhibiting (through the end of April) the artwork of local digital artist and author, Bruce Rawles. Inspired by line art in a book by fellow UK author & geometer, John Martineau, Rawles' 3D computer rendered images incorporate NASA imagery as well as nature photography as backdrops to stunningly accurate (most 99.9% or better) models of our solar system that pick up where Johannes Kepler's explorations left off. Framed archival giclée prints as well as larger posters, card and books will also be available at the First Friday event at the Mobius.

More information about Rawles' "Martineau Series" is available here.

This award-winning exhibit was recently shown at ScienceWorks in Ashland, as well as the Rogue Gallery, and has also appeared at galleries in California, Switzerland and Austria. More information about Rawles' "Martineau Series" exhibits and other presentations, etc. is
available here.

Rawles is also the author of Sacred Geometry Design SourceBook, published in English and German as well as co-author of a geometric screensaver and meditation tool based on ancient laws of nature
He maintains a
blog about a variety of related interests.

Green For Free ECOnomic=ECOlogic checklist

Thanks to Marge & Janaia of Sierra Nevada Deep Ecology Institute for emailing a great ECOnomic=ECOlogic checklist, courtesy of Solar Cascade. Although most of us are already doing many of these, a refresher is always good, and some neat new ideas here too... Rather than print out this liks, try email first, and print only if necessary... (I keep a supply of 8.5" x 11" scratch paper I get from rough drafts and mistakes as well as 'tree spam' a.k.a. junk mail on top of my printer for things that really must be printed (maps with complex driving directions, etc.)

Another Step 3 addition might be to suggest long range lifestyle, community & career planning that allows walking/biking to work/telecommuting as the norm rather than the exception: web & internet-based livelihood (with generous walks & outdoor time to balance out the glued-to-the-monitor hours) seem to be contributing to that idea becoming more widespread. If best practices are integrated into everyday, it's no big deal! Happy



Worthwhile Yoga Videos & Breathing

Thanks to many teachers (most of whom I either have lost contact with or don't recall their names) who have given me introductory instruction in basic stretching and yoga postures... and breathing! Happy

Speaking of Breathing, I've found these breathing techniques quite simple and practical to use when wants to emphasize a particular element (e.g. focus on water when one needs to cool down, focus on fire when one wants to warm up, focus on earth when one needs grounding, or air when one could use some uplift and inspiration. Thanks to
James who gifted me a copy of this Puran Bair's book, Living from the Heart, which suggested these element-breath associations... try them! Happy

Fire (In: mouth; Out: nose)
Earth (In: nose; Out: nose)
Air (In: mouth; Out: mouth)
Water (In: nose; Out: mouth)

Here are a couple of videos we checked out of our soon-to-close
that are great for perennial novices like me...
Basic Yoga Workout for Dummies, and Yoga For the Young At Heart - Accessible Yoga for Every Body.

Flower of Life grid at different sizes

Thanks to Andrew M. for alerting me to this lovely illustration that appears to be a hand-drawn Flower-Of-Life variation with overlapping scalings... neat!

Beautiful Symmetry-E8 computation

Although the math is a bit beyond my conscious fathoming, I find the idea that there is a collaboration exploring beauty and symmetry in higher (would you believe 248?) dimensions ... and finding it! ... to be a satisfying notion Happy Here is a link to "E8" research and a "string art" visualization.

Great Start to Earth Month - Wangari Maathai

I watched an inspiring interview on Link TV featuring Wangari Maathai, who started by planting 7 trees in Kenya. That number grew to over 30 million, by paying women 4 cents per tree to plant and keep them alive. Her Nobel Peace Prize was justly deserved; she demonstrates the principle of interconnections between ecology, economy and community in wonderfully pragmatic ways.