"The MAPS 2006 Psychedelic Calendar was a special publication produced by the Multidisciplinary Association for Psychedelic Studies (MAPS) to commemorate their 20th anniversary and the 100th birthday of LSD discoverer Dr. Albert Hofmann." AI Overview
"The "Pentagon Tile" artwork by Alexander Braun served as the cover art for the MAPS.org (Multidisciplinary Association for Psychedelic Studies) 2006 calendar. This special calendar edition was created to commemorate the 100th birthday of Dr. Albert Hofmann, the Swiss chemist who discovered LSD.
- The Piece: The featured cover image was Braun's first full mandala painting of his unique pentagon tile design, created using fluorescent acrylics on a large 60" x 60" canvas.
- The Design: Created originally in Toronto on December 28, 2004, the artwork highlights a geometric, fractal golden-mean structure. It utilizes two specific types of golden ratio isosceles triangles (with angles of 36°-72°-72° and 108°-36°-36°) to resolve the "unaccounted space" usually left when trying to tile regular pentagons on a 2D plane.
- Exhibitions & Legacy: Before being selected for the MAPS.org calendar, the physical canvas was exhibited at the Museum of Contemporary Canadian Art (MOCCA) in 2005. Between 2006 and 2008, Braun also adapted this specific fractal pattern into a silkscreen design to create hand-made t-shirts." AI Overview
I have designed a pentagonal tessellation back in December 2004, challenged by a friend to try to tile pentagons, inspired by x-ray photo of a quasi crystal's atomic refraction which I have extrapolated into pentagonal tessellation by literally connecting the lines between the points and figuring out the golden ratio math behind it.
Here is the image of my original painting of the Pentagon Tile, the Colour Wheel series 1 (2005) which was displayed in a group show at the Museum Of Contemporary Canadian Art (MOCCA 2005) and published on the cover of the 2006 calendar by Multidisciplinary Association for Psychedelic Studies (MAPS) in NYC, USA.
My pentagon tile painting was published on the cover and I was invited to come to Switzerland for a centennial birthday part which I couldn't attend, however since then all images of the original 2006 MAPS calendar were removed from the internet.
My studio manager / art dealer at a time was Fred Crawford who has organized it with the MAPS by submitting my 60"×60" painting of the first pentagonal tessellation colour wheel in the global call for art contest. I got also a congratulatory letter from MAPS on being accepted on the cover and have received one copy of the calendar. I will try to find the letter, the calendar is lost yet I have some pictures of it. Make of it what you will but it smells conspiracy. Anyway, it is very strange indeed.
Original PR:
New pentagon pattern discovered by a Toronto artist.
It is impossible to tile a pentagon with the same size pentagons in 2D plane without leaving unaccounted for space. By many many attempts were made to come up with a way to tile this basic geometric shape and some were successful, others managed to design nice images containing no tile pattern algorithm.
On December 28, 2004, I was visiting my long-time friend Yehudah Lionel Cullman who showed me an [x-ray photo of a quasi-crystal] forming five-sided symmetry in a science book and said, that as far as he is aware there is still no known way to tile a pentagon. Inspired by an x-ray picture and challenged by a mystery of the pentagon tile I started to chart my attempt at the impossible. I have realized that the only way to tile a pentagon with only one size pentagons would be in 3D forming the fifth Platonic volume - dodecahedron (i.e. "two plus ten faces" in Greek), where the twelve pentagons enclose 3D space. Still, curious, I decided to try to design a pentagon pattern.
I have noticed that at the centre of quasi-crystal photo were ten dots forming pentagons aligned in a perfect circle arranged as a ten-pointed star. The fact that here I see ten pentagons in a circle gave me an idea that if I only tile 1/10th slice of it, which is 360/10=36 degrees, then it would be enough to create a tile pattern.
So, I drew one 36 degrees slice of infinity and placed one pentagon at the bottom corner of it where it perfectly matches the 108 degrees of the inner pentagon angles. The rest came in place naturally, as I just continued the pentagon lines to determine what other basic building shapes of the tile are there at the very bottom of the pentagon slice. Then I have discovered that only two isosceles triangles in golden mean to each other, with angles of 36'-72'-72' and 108'-36'-36' degrees, form the pentagon tile pattern. Therefore these two triangles can form a pentagon, or a star, or a perpetual fractal pentagonal pattern.
The main dilemma for many who have tried to organize pentagons in a pattern is what to do with the unaccounted for space. In my attempt at it I have soon realized that the unaccounted space between pentagons when tiled within the 36 degrees slices form perfect stars, pentagrams, which makes total sense since it is the shape contained within the pentagon boundaries. The next challenge was to figure out the actual tiling algorithm of the pentagon tile's perpetual expansion of its infinite outer rings. I realized that whatever happens at the bottom is what happens at the top of it, only on a different scale. Soon I noticed that the ring of pentagons is followed by a ring of stars and then by pentagons again in a perpetual rotation based on the power of six, i.e. 6x6x6...:
* 1, * 6, * 36, * 216, * 1296, * 7776, * 46656, * 1679616, * 60466176, * 2176782336, * 78364164096, * 2821109907456, * 101559956668416,
etc."
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