The aggressive carnivorous reptiles in this tessellation are based on Roger Penrose’s “Jigsaw Puzzle” tiles. The reptiles form closed circles, facing alternately inwards and outwards.. It seems impossible to hold all the circles in view at once, instead by shifting attention, one can see clearly only the olive, ochre or green circles at any one time.
Doris Schattschneider, in her book Visions of Symmetry, describes Penrose sending his Jigsaw Puzzle tiles to Escher as a wooden puzzle as a challenge for him to solve. Escher was successful, and eventually produced “Ghosts” his last symmetry drawing in 1971 based on the tiles. It is probably one of Escher’s least exciting tessellations and shows the challenge in the restrictive edge matching rules inherent in complex tilings. The tiling is anisohedral, with only a single edge profile used, although in mirrored form.
The reptiles are identical in shape, but appear in mirror image. In each tile the edge profile occurs in mirrored orientation too. The tiles use a single edge profile for all parts of both lizards, hence the rolled up tail, which in nature is possessed by chameleons, presumably the docile ancestors of these strange, aggressive beasts.
Thanks to the ArtScience Museum for a fascinating afternoonon Saturday 24th September. It was intriguing for me to hear such divergent views of Escher from the speakers. Presenters were Federico Giudiceandrea , Curator of ‘Journey to Infinity: Escher’s World of Wonder’, Dr Sai Kit Yeung, Assistant Professor of Vision, Graphics and Computational Design (VGD) Group in SUTD, Angela Liong, co-founder and Artistic Director of ARTS FISSION, Maria Kozhevnikov, Associate Professor of Psychology at NUS, and I was very pleased to be included too!
I found Maria’s presentation very enlightening. It showed how different people use one of two different visual processing systems in the brain, and the data she presented was fascinating, and to me, aligns very closely with the differing status afforded Escher by the world of fine arts, and the world of science. And as architects were one of the few professions that use both systems, explained why I enjoy Escher so much, and enjoy making tessellations.
The afternoon was expertly moderated by Honor Harger.
The exhibition at the Marina Bay ArtScience Museum opens on Saturday 24th September.
Fish Scales III is the last exhibit before the gift shop.
The exhibition is really good, with a series of very interesting rooms organised by theme, and in a surprising series of pastel colours derived from the prints and watercolours, which actually work very well with the predominantly stark black and white prints.
Fish Scales III Detail
Bigger and Smaller (which is much smaller!) is next to it:
Coming from a family of bad pun makers, this idea was irresistible; it combines a word game with a visual game. A Pen (a medieval quill in this case) and a Rose tile to make an enormous bouquet of Penrose Tiles. The perimeter of the tiling is a continuous linked row of pens, perhaps the tessellation is drawing itself, like Escher’s famous Drawing Hands.
While roses don’t present such a tessellating challenge as creatures with arms and legs, they do nicely bunch together, like florist’s roses wrapped in cellophane. And the entire print layout is quite rose-like too, with 5 large petals of tiling opening up.
Pen-Rose print detail
Here in Singapore Hoya plants grow in the trees, a tropical relative of the humble milkweed. They form balls of closely packed pentagonal flowers, here is one from my garden, it has some close similarities to the tessellation:
Sha Kua Detail
In this tessellation, sharks arise from the deep sea vents and circle menacingly at the surface. The name of the tessellation refers to the Ba Gua, a Chinese religious motif incorporating the eight trigrams of the I Ching, arranged octagonally around a symbol denoting the balance of yin and yang, or around a mirror. In this case it is printed on a reflective silver aluminium panel, so is both mirror and motif.
Cellular Chess I
Cellular Chess I, II and III
These 3 prints are based on 5, 7, 9-fold geometry, and use a similar tile design to create a pattern that makes a flowing checkerboard. Cellular Chess I is based on 7-fold geometry and uses 3 rhombi, Cellular Chess II is based on 9-fold geometry and has 4-rhombi, while Cellular Chess III uses the 5-fold geometry of the Penrose Tiles. It would be interesting to see what kind of chess game could be played on such a complex board. The gold version of the print has a circle of gold in each alternate cell.
In each case I used a substitution technique to generate the patch of tiles, then selected a portion of the tiling that has a regular outline, but is quite irregular on the inside, without rotational symmetry. For the set of prints, I looked for a shape that would give me cells of approximately the same size, and then find a regular shape of similar sizes for the overall design.
What is interesting, is that each tile-set has its own “gestalt” despite having the same basic pattern. The 5-fold is quite axial and feel stiffer, while the 9-fold is much more flowing.
On a recent trip to the deep south of Western Australia, I came across the most beautiful ripples in the soft powdery sand, and they struck me with their similarity to these patterns.
Cellular Chess III based on five-fold geometry
Cellular Chess II based on nine-fold geometry
Frog Star III
Big and small frogs are closely packed into a star formation. Based on the Kite and Dart version of the Penrose Tiling, the red-eyed frogs are coloured in gold, teal and green. The entire star is also rather frog-like..it is easy to see the five-lobed shape as having a head and four webbed feet. Whilst the print has 5-fold rotational symmetry, the colouring using 3 colours does not.
Frog Star III is the aluminium version, a Dibond print on routed aluminium panel around 1.2m in diameter. It is based on Frog Star I, a print that was presented to Roger Penrose in 2007. He kindly said it was the best tessellation he had seen based on his tiling.
Frog Star II is a smaller version on paper, around 0.7m in diameter, using less tiles, and is contained within Frog Star III. It has hand-applied gilding.
These fish are schooling, and in their frenzy form a special formation. The tessellation is made from a single tile design, and appears in mirrored as well as regular orientation. Two different shadings, and 3 colours, create two interlocking figures, dark and light, a figure known as the Gosper Flowsnake. The fish have a bright lateral line, this line traces out the plane-filling Gosper curve, from the lower left to the lower right. The fish inhabit a watery universe which has two flows of dark water and light water, the dark and light swirls grow out of these bodies of water.
The version shown is the aluminium version in golds and reds. A detail of the paper print version in greens and blues is below.