Search Results for: spiral

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.

Spirals, Ferns, and Universal Unfolding Motifs

Thursday, 1 December 2022 by Bruce Rawles

While I try not to obsess about geometric forms, I do observe when certain motifs appear more frequently in various locales. When we visited San Miguel de Allende, Mexico earlier this year, I noticed an abundance of small stellated dodecahedra (and similar shapes) particularly evident in metal lamps, yet also in other art forms as well; each pentagonal pyramidal stellation arm encodes the golden ratio. …

Having just returned from a second visit to New Zealand, it seemed that one of the most ubiquitous geometric shapes we saw on this trip was the spiral, which appears in Maori jewelry, carving, tattoos, art, and culture, connecting the natural world with the art of the indigenous people of Aotearoa. Below I made a mirrored tiling pattern from an image of an unfurling silver fern frond which exhibits an excellent example of fractal geometry.

Wikipedia says “The koru is a spiral shape based on the appearance of a new unfurling silver fern frond. It is an integral symbol in Māori art, carving, and tattooing, where it symbolizes new life, growth, strength, and peace.”

Reflecting intuitively on our spiral “journey” through life like the homeward trajectory Dorothy embarks upon in the Wizard of Oz when she follows the yellow brick road, we find context in the cyclical, yet ever-evolving, ever-unfolding awareness with each revolution of the spiral. In three dimensions, we have the double helix of the DNA molecule in everything we typically call life in this world, embodying the golden ratio in each pentagonal molecule appendaged to the helix and also in the (Fibonacci proportion) 34/21 Angstrom ratio of each complete turn of the helix. Every year, each season has familiar patterns and signs, yet there is a much larger progression we discover when we “zoom out” a bit from our myopic, provincial perspectives. The Chambered Nautilus shell has a pleasing uniformity as one spins the shell around, since each accretion uses the same angular template as the preceding one, and builds upon the strength of sameness throughout.

Here are a few more spirals from our most recent NZ trip; enjoy!

New Zealand: Napier museum; Maori wood carvings with numerous spiral forms

Auckland Airport ceiling lamp fixture — Auckland NZ Airport ceiling lamp fixture

Auckland NZ Airport ceilng art: spiral fish school

New Plymouth, NZ art gallery staircase; spiral flourishes

Napier NZ boardwalk art with overlapping complementary spirals

Golden Spirals and Golden Angles

Saturday, 29 April 2017 by Bruce Rawles

Further fun Fibonacci forays for fascinating Phyllotaxis? :-)

The Art of John Edmark | Talk by Paul Dancstep | Exploratorium

The magic of Fibonacci numbers | Arthur Benjamin

John Edmark – Math X Art

Here’s a prior GeometryCode.com post featuring Edmark’s elegant geometric sculptures

Spiral shell sculpture

Friday, 24 October 2014 by Bruce Rawles

Sculptor, fellow artist, geometer and student of metaphysics, Stefán Geir Karlsson recently sent me some interesting conceptual images and commentary about making some really large spiral shell sculptures. His virtual vortices would be fun to explore as full size realized art forms. He says, regarding the first image below, “This is a photoshop in front of the new opera house in Reykjavik (Iceland).” Enjoy!

“Below is 1 foot model from granite” next to the shell he modeled it from.

“I have been obsessed with the Conch Shell since I was a boy. My dream is to make one
that you can walk into either from stainless steel or granite.”“As a boy I always wanted to know how it looked on the inside. So I would very much like to make one you can walk into. I know all kids would love it. I know people in China that have the skills to help me do it.”

I’ve long had similar ideas for making huge models of polyhedra with mirrored interiors that we could walk inside, see the labyrinthine reflections and hear the equally fractal echoes; all metaphors of our projections mirrored back to us! :-) Colleague Sara Frucht of Berkeley, Calif. has some excellent smaller models she calls ‘Kaleidoscapes‘ with wonderful interior mirror reflections.