Blog

Fractal flotilla? Topological temple? Self-similar shrine? Growing options for fractal art

Monday, 28 June 2021 by Bruce Rawles

$IMception: fractal flotilla?$

This intriguing image is among those featured in this article about a Kickstarter campaign – by Raksha Singla, creator of IMception, a new project which aims to add a newcomer to the existing field of fractal generation software:

“This exciting new program on Kickstarter is a gateway for an eternal journey into the world of fractal illustrations. It is so simple to use that anyone can instantly become a confident artist.”

Here’s a related article with some current options for making your own fractal artistry: Ultimate Guide to Fractal Generators: The Best Fractal Software in 2021 (Free & Paid)

Here are numerous prior posts on the GeometryCode website that reference fractals.

Kinetic Geometric Art

Thursday, 6 May 2021 by Bruce Rawles

The dimension of time coupled with the other three spatial dimensions can add tremendously to the potential of geometric art as exemplified in these kinetic sculptures. We first looked at David C. Roy’s kinetic sculptures a few years ago, and this video provides an enjoyable update on his mesmerizing moving mandalas… and other kinetic art which leverages lots of talents including geometric sensibilities.

Moving further into full 3-dimensional kinetic art, here are more lovely examples of moving geometric art by artist Ivan Black. Among many other exquisite designs in this video, if you always wanted to see the (Fibonacci Spiral) “Whirling Squares” animated in 3D, check out this outdoor, wind-driven yellow sculpture which starts about 9:17 through about 10:03 into the video; gives new vitality to the “whirling” adjective! :-)

… and in case you missed it (or would like to be wowed again), here’s a link to a prior post from this site that links to Blooms: Phi-Based Strobe Animated Sculptures that heterodyne rhythmically in dazzling fashion, benefitting from the use of stroboscopic light applied to rotating forms with golden ratio proportions.

Sketches in Code: Randomness and Patterns in Science and Art – Livermore, CA exhibit

Wednesday, 28 April 2021 by Bruce Rawles

While visiting my hometown of Livermore, California this month, I was fortunate to see a very well done exhibit in the lobby of the Bankhead Theater entitled “Sketches in Code: Randomness and Patterns in Science and Art” which featured several interactive exhibits as well as numerous examples of 2D and 3D art, many of which will be familiar to those of us who have studied these realms for decades. Here is the detail from the Livermore Arts website:

Science, math, computers and art meet nature Explore how the intersection of mathematics, science, art and computers can be used to visualize and create artistic pieces which also describe and explain nature. As you tour this exhibit, we hope you see that, while art has often been described as an opposing discipline to mathematics, science and computers, in many ways they are very similar. In the end, all are creative processes that involve a journey of discovery. This exhibit is co-sponsored by Livermore Arts and Quest Science Center Bankhead Theater Gallery Feb 12–May 2 Open Fridays 2-6pm; Sat and Sun 1-5pm Limited entry, masks required. Family-friendly interactive exhibits with Covid protocols in place. Join us for this (exhibit) of science-meets-art.

If you’re reading this before May 2, 2021, you may still have time to see the exhibit in person if you’re in the San Francisco Bay area; recommended for the entire spectrum of those completely unfamiliar with the subject to those well-versed. Here are some cell phone photos of the exhibit items (most self-explanatory):

The first two photos are of a particularly nice 3D printed Sierpinski Tetrahedron (fractal tetrahedron) at the top of this article, with the second photo being a fun interior view with a pentagram-like interior contour:

If you’d like to make a Sierpinski Tetrahedron – a great geometry classroom or home school project! – here’s a fun sped-up how to video: (which also demos the same idea for a Menger Sponge.

$examples of fractals$

$fractal examples$

$fractal branching$

more mirrored polyhedra

Thursday, 25 March 2021 by Bruce Rawles

Over the years, I’ve been fascinated with the exquisite possibilities of using mirrors for the interior faces of polyhedra (particularly Platonic Solids and Archimedean solids, and among those, particularly ones with dodecahedral and icosahedral symmetries.

One of my earliest fun discoveries was the Kaleidoscapes work of colleague Sara Frucht. She showed me some amazing reflected interior spaces made simply by using 3 triangular mirrors with a shared vertex, carefully designed to replicate the interior angles of a variety of polyhedra.

There are a number of other examples I found over the years by other geometric artists and this latest exhibit at Melissa Morgan Fine Art in Palm Desert, Calif. featuring the geometric artwork of artist Anthony James is quite stunning. I would check it out if I lived closer to southern California! :-) It appears that he’s using uniform edge lighting (probably LED that wasn’t available not too many years ago) and 2-way mirrors to make particularly lovely 3D models that can be viewed from many angles. Here are additional photos and a short video of this exhibit.

I’ve seen other versions (including a dodecahedron at the Exploratorium in San Francisco, California several decades ago) which used regular (100% reflective) mirrors for all but one face, with the one “viewing face” either open (affording putting one’s head inside the shape for an even more immersive experience) or with regular glass.

When the Olympics was held in Greece some years ago, I thought it would be a cool attraction (with homage to the home of both Plato and Archimedes for whom their respective polyhedra are credited) to have huge versions of the aforementioned polyhedra big enough to walk inside (perhaps with elevators bringing spectators in and out) and then an additional bonus would be making acoustic recordings inside each of these structures and having a multisensory experience enhanced by the unique acoustic resonances of each structure, much as Paul Horn did with his classic recordings of flute music in the Taj Mahal in India and the Great Pyramid in Egypt. I made a very short recording inside the latter structure in the fall of 1992.

Here’s a video about another seasoned artist (Frank Stella) who has incorporated – appropriately enough, given his last name! – stellated polyhedra in his work.

Tetrahedron Volcanic Points on our planet

Sunday, 28 February 2021 by Bruce Rawles

On this page (Sacred Geometry Design Sourcebook – sample – (page 224) Star Tetrahedron Fold-up Pattern), I made a table with a handful of map locations (latitudes and longitudes) that seem to (mostly) have volcanic features; I recently made a google map for a web client as a demo and then made another map of some fun places we visited in New Zealand a couple of decades ago. So now I’ve made a map of these “volcanic points” that correspond to points where a tetrahedron (actually a star tetrahedron)* would intersect the sphere of the earth. (No I didn’t calculate the minor latitude change that would account for the fact that the earth is actually a spheroid – slightly flattened at the poles, but these latitudes should be fairly close.)

* If one places one vertex of a tetrahedron on the north pole, the other 3 vertices would all be at about 19.5° South Latitude; If one places one vertex of a tetrahedron on the south pole, the other 3 vertices would all be at about 19.5° North Latitude, which you can see in the map below; the longitude points vary.

If I recall correctly when we were on the big island of Hawai’i years ago, a park ranger explained that the active volcanic activity over millennia has made the entire Hawaiian Island archipelago, but the location of the active lava formation remains at the same latitude. This would seem to confirm the fixed latitude of these “fire points” as Plato might describe them.

Speaking of maps, here’s a recent interesting NYT article about the ever-popular attempts to try to convey 3D in 2D and minimize the distortions inherent in that attempt: Can This New Map Fix Our Distorted Views of the World? I’m glad I noticed this link in the article to an interesting archive article about Buckminster “Bucky” Fuller’s Dymaxion map of the earth. If you want to try living in a geodesic, visit colleague Asha’s Pacific Domes website.

Of course, higher and higher frequency flattened geodesic nets (a.k.a. fold-up patterns) give less and less distortion, but at some point, we might well ask ourselves, why lose perspective by going to fewer dimensions and less complete and inclusive information? Our tiny view of the world is necessarily hopelessly infinitesimal, but our Inner Vision can transcend the apparent limitations of space, time, and specifics. :-)

Here’s a photo of Bucky Fuller holding a cuboctahedron – an earlier map concept; the icosahedron having more faces works better. Here is what Wikipedia says about the Cuboctahedron: “Fuller applied the name “Dymaxion” to this shape, used in an early version of the Dymaxion map. He also called it the “Vector Equilibrium” because of its radial equilateral symmetry (its center-to-vertex radius equals its edge length)”