I have been exploring dimorphic tessellations for the past couple of months and following my Twitter post on the subject created the goose motif. It appears to tessellate the plane as D1gg and D1Kg but I am not certain these are the correct groups. Please comment if you know for certain. I started with a "J" shaped tile which was based generally on the shape of Bermuda. After several iterations it became a more refined shape and I made a cut out cardboard model to make it work. There are three figures below; the first figure is the final design on graph paper; the second two images are of the motif tiling the plane. All three figures are watercolor, pen and ink and colored pencil.
A simple P3 rotation of a great white shark motif. This is a watercolor, colored pencil and ink drawing. I couldn't resist the reference about the "Finding Nemo" encounter with the Great White Shark (e.g. "Name's Brucie"). Hope you enjoy it. I had a lot of fun creating the tessellation.
The glide reflection motif of jet airplanes in this image was created a few years ago. I referenced it in an earlier blog. It was inspired by a flyover and roll from two F4H Phantom jets when I was about ten years old and working in the garden at my grandparents home in Indiana. It was like a private air show! The pilots must have seen me waving my garden hoe feverishly in the sunlight from a distance and as they flew over they did a roll for me no more than a few hundred feet from the ground! I could see the pilots in the cockpits. That was a very cool thing they did for me. I was yelling and my grandmother came out of the house to see what the commotion was all about. For this drawings I had been working on an idea that had a farmhouse and a garden below the jets but that idea didn't seem as interesting as the jets flying in opposite directions with contrasting backgrounds out of the page. So I combined the glide refection motif of the jets with a landscape and mirror reflection of a village in the background. I drew this design on mylar with Stabilo pencils.
The motif of Alice, the Red Queen and the Cheshire Cat is an early tessellation I created in 1980. It’s a throwback to another artwork I gave away called “The Ubiquitous Smile” and has been lost. I had saved nothing from that original drawing (watercolor) other than the two sketches/scraps below.
I chose to redo this image for one reason; the story involves one of my engineering professors that originally inspired me to do the expansion and morph the image the first time around. This is for Aldo.
Dr. Aldo Giorgini was a gifted mathematician, computer engineer and civil engineering professor at Purdue University where I met him; taking two classes from him - hydraulics and probability and stochastics for civil engineers. I took these classes in 1981 and 1982. Aldo was brilliant and I was not a great student. He graciously met with me and patiently gave me some mathematical pointers on how to expand and distort the Cheshire Cat figure. Aldo was one of the earliest artists that created computer art. Working with FORTRAN and writing his own code. If you are interested in early computer art - and I mean early, circa 1973, there is a great book by Esteban Garcia Bravo, entitled “Cybernethisms, Aldo Giorgini’s Computer Art Legacy”, Purdue University Press, 2015.
So this image is a remake and is a pen and ink, colored pencil and watercolor on Twinrocker paper. The original tessellation from my folio is below as is the pen and ink I discussed with Aldo. Hand scribbles on side are mine. Somewhere I have some handwritten notes with mathematical notation from Aldo on curve fitting but alas I have misplaced them. ( I had them out for inspiration to create this no more than three months ago- go figure! Had them 38 years and just now lost or misplaced them! )
This is a very old motif that goes back to 1980. It was actually my second tessellation motif. It predates the internet, AutoCad and cell phones. My first drawings of tessellations were done before I owned a light table and were traced from a drawing onto frosted mylar to repeat the figures as closely as possible. The original drawing of this image was lost. I worked up a new image and again chose to draw it on frosted mylar but this time I also used a light table to move the figures around the stairs. I used a Black Stabilo pencil to create the drawing.
The figure below is of the original Wizards and Trolls motif on Ingres paper.
The following is a horse tessellation as a P4. The pencil study is below as is the final drawing in watercolor and pen and ink. This is a new motif that transforms or rather replaces a running horse with a flying motif.
The angel motif was created in November 2019. I haven't used it in a drawing to date but the watercolor of the pure tessellation is below. While faith, hope and love eternally reigns, Easter this year, reminds me of the poem by W. B. Yeats, "Easter 1916". There's something palpable about the words to the poem this year and several stanzas seem relevant even if written with totally different intention and meaning then.
"He too has been changed in his turn,
A terrible beauty is born."
Just as the words terrible beauty do not seem to go together in one phrase the words social distancing are an oxymoron.
The Minotaur has been a mythological creature for centuries. I remember reading about Theseus and the Minotaur many years ago during a class in literature. I made an attempt to create a small development design with the Minotaur motif. The motif grew out of my interest in mythological creatures (Icarus, centaurs and griffins etc.). I had always been a fan of the movie "The Labyrinth" since the movie used a set configured like MC Escher's "Relativity". The motif is very recent from November 2019. I decided to make a pen and ink drawing of it.
The basic design Idea was from one of the Figures in Structural Topology No. 15. The Journal was given to me by Jeffery Price from Artists Market in 2016. The paper "Super and Superb Colourings of Tilings" by Geoffrey Shepard discussed isohedral tiling and multiple coloring schemes. The mapping and mathematics in this paper is beyond my understanding but I used the IH28 tiling in black, white and gray for this motif.
Below i am attaching a pencil drawing of the development and a pen and ink drawing. I've been able to spend some quality time in my studio over the last month. Its been good to be able to reduce my back log of ideas and draw and paint much more than i have over the last year.
The figure below is a metamorphosis that was developed over several months. It includes eight (8) tessellations. Rotation (P3 Greek Soldier)-->Rotation (P3 Turtles)-->Rotation (P3 Cardinals)--> Rotation (P3 Frogs)--> Translation (L1 Butterflies)--> Glide Reflection (L2 Flying Horses)--> Translation (L1 Achilles, Tortise)--> Rotation (P3 Icarus). This image is 7-1/4 inches wide by 28-3/4 inches long. It was big enough I couldn't do it as a stone lithograph so I drew it with pen, ink, and watercolor on paper. Its dedicated to my colleague M.C. Escher. Even though we never met- I enjoy walking into and exploring the garden. Those of you that read any of Escher's writing will understand what that means. I have an immense amount of respect for his intellect, creativity and graphic design.
Its been quite awhile since I wrote a blog. The image above is of a P3 tessellation that has been translated to a hyperbolic image. I originally completed the Icarus image in 1986 and did it on a lithographic stone and printed it. You can see that in the print called Metanoia (see Tessellation Art Gallery Page 2). I made that original print in the studio at the University of Wisconsin at Milwaukee with Mark Wilson as the instructor. I also made the Icarus tessellation into an etching called Michael's Dream (see Tessellation Art Gallery Page 1) and hand colored it. The above image was drawn on lithographic stone to make it into a new print. This is a photograph of the line work on stone. This is the second hyperbolic tessellation I've completed. The first was Flying Fish 2020 you can see that on the Gallery Page 1.
The basic geometry was constructed with line and compass and then I traced over that onto tracing paper using a light table. After several adjustments (actually numerous) I transferred it to stone. It was very time consuming to draw as each image is drawn by hand (Polychromos pencil) after transferring it to stone with iron oxide paper. I hope to print a color background and do some 3-dimensional shading work to finish it off but for now I'm satisfied. I'll print this stone at Muskat Studios. (www.muskatstudios.com). I've been collaborating with Carolyn Muskat for 20 years now since completing the image War and Peace at the MFA School back in 2000.
I enjoy working the stone and get a great sense of satisfaction as the image materializes and then pulling the first proofs. Drawing on the stone is a unique feeling and has a smoothness and coolness even if its old technology. I really enjoy it.
The images below are of two tessellations designs I have had for a number of years. The frog tessellation dates back to 2001 an the bird tessellation dates back to 2006. The black and white images are visually very appealing and crisp. Figure 1 is Frogs. Figure 2 is Birds V.
I've always been impressed with the way pure black and white images come off the page. Andrew Crompton has created some very impressive back and white tessellations and has previously made some suggestions to me about ways to enhance my images. I like the graphic style and the straight lines and angles that he uses in the hashing of the black against the white. In contrast to the pure black and white the colorful images, beautiful line work and organic shapes that Francine Champagne has done on her website are very expressive and grabs your attention. The dragon tessellation she has created through exploring pentagons is remarkable. She's also given me some pointers on using KaliedoPaint.
The images I am attaching here are three hand drawn, pen and ink black and white images and the first image I created on KaliedoPaint- which is very basic. I am working on learning more about computer generation of tessellations and hope to add some to my blog in the future but I am sure I will continue to design tessellations by hand as well.
The design of a metamorphosis as a tessellation is very challenging. There are limited examples of these types of tessellations. Escher was unquestionably the best and created the art form with lifelike tessellations. I have created some smaller designs with one motif that transforms but is technically not a metamorphosis. While I was working on a new motif a few weeks ago I noticed that the image I was making was similar to a previous bird image. The creation of Development IV began in earnest. I wanted to have at least three forms that changed. This metamorphosis is a combination of three designs; a lizard, a bird, and a frog and seahorse. I began to think about how I could depict the "desert to the sea". So the image began with the horned lizard motif in the desert and transformed into birds and then into frogs and seahorses. I choose to depict a Sargasso Seahorse. The Sargasso Seahorse is one of the strangest looking and best camouflaged creatures in the world. It has long appendages that look exactly like the seaweed in its habitat. Its virtually impossible to distinguish the seahorse from the Sargasso seaweed. Of course my representation is generalized and not as fabulous looking as the real thing.
Development IV was done in ink and watercolor. I'm planning on working on another much larger metamorphosis design that I started a couple of months ago and showed a sneak peek at the demonstration I did at the Museum of Fine Arts.
Try doing a metamorphosis design its very challenging but when you get an image you like very satisfying. Figure 1 below is Development IV. Figure 2 below depicts the original pencil sketch of the tessellation. I made some changes to the design as the drawing progressed to final design.
This blog shows several examples of small works I have recently completed. All of these prints are less than 3 inches by 4 inches in size.
The smallest linocut "Black and White" (2 inches x 2 inches) depicts two stylized sting rays with insets of two smaller rays. I liked the motif and since it reproduced well choose to print it in black ink.
The second motif is called Fish and Frogs and is 2-3/4 inches x 2-3/4 inches. Its a linocut in black and white. This motif is a little more complex but still rather simple. The idea came from a sketchbook drawing from several months ago.
The third motif is my first woodcut which I finished in late 2017. I am still working on my woodcut technique and used a basswood block with gouges to print the block. I called it "Four Dragons". Its 3 inches x 3 inches in size and I choose black ink. The motif comes from one of my P4 tessellations called "Happy Dragon" and is a stylized Chinese Dragon.
The fourth small work is a color linocut called "Star of Wonder" I did it as a Christmas Card last year and decided to make a simple 3 inch x 4 inch print. The colors were printed from smaller portions of blocks I cut out of the full block.
The last figure below depicts the linocut blocks for the two smallest prints and shows their size next to a quarter. Overall I was pleased with these efforts since they didn't take that much time to complete and print. I probably spent no more than a couple hours on each of the linocuts and maybe a little longer or up to three hours on the woodblock.
My first designs for tessellations were done on frosted mylar in the very late 1970's and early 1980s because it was the easiest way for me to copy the motif without a light table. I entered one of these early drawings in the Indiana State Fair in 1979 and got an Honorable Mention. Three or four of these early designs were lost or given away and I did not keep copies or records of them. One of the earliest but not the first is the Figure 1 below. Its a two figure tessellation of one of the designs I drew and gave away on mylar to a friend that worked in a gallery with me in the summers while in college. This design is one of the few that survives from 1979 on watercolor paper. In 2017 I decided to recreate the original drawing or redraw the original to the best of my recollection. Figure 2 is a drawing on tracing paper of "Searching for Clues". Its an example of my earliest types of designs which were more drawing than tessellation as I was just beginning to understand the way that the various symmetry groups went together. I am still trying to decide if I want to create a lithograph of this drawing. Right now I am just satisfied that I was able recreate the drawing.
I recently completed two (2) artist demonstrations on my tessellation techniques at the Museum of Fine Arts Boston on February 11th and February 14th. These demonstrations gave me an opportunity to interact with other Escher enthusiasts that had recently visited the exhibit in Gallery 155 ( over 50 of Escher's prints and drawings are on display! ).
I was able to work through several new designs and explain my process over a total of about 5-1/2 hours. One of the new prints I showed was a stone lithograph of a new winged horse motif. MC Escher's print Horsemen (No. 342) is arguably one of his best woodcuts. It combines the iconic and complex Horsemen motif which is a D1gg symmetry family within a masterful three color design as a flattened Moebius strip. The key to the D1gg is the beautiful glide reflection of the motif and the interlocking of the tessellation as it alternates left to right and right to left. Another aspect is it's very pleasing to the eye due to the color contrast. Color choice and contrast are critical to the aesthetics of tessellation. Overall Horsemen is one of my favorite and certainly in the top ten.
My attempts at an interesting D1gg motif go back several years. Most of these attempts I dismissed because they were not that articulated and just not good enough in my view. The Horsemen II and Lizards (2017) are nice but are not that much different than Escher's motifs. I created my first flying horse (Pegasus) tessellation in 2001. Since then I have modified it and made different versions in the C1 symmetry family (see My Tessellation Art Gallery page 2 Pegasus II) however I always wanted a flying horse as a D1gg glide reflection. See Figure 1 below. This new motif is a rare example that successfully accomplishes what I wasn't able to do previously and can be easily drawn as a Moebius strip. Hope you will try your hand at some D1gg's they are an elegant symmetry family and there's a number of great designs and drawings that incorporate them.
A second new motif was shown as a linocut. It was an interlocking sea turtle and fish motif. My inspiration for this design came from a family vacation to Bermuda where we saw sea turtles and many reef fish. Figure 2 and 3 depicts Bermuda and the original drawing.
I also had several activities (see examples) at a table that could be completed at the event or later at home. My goal was to make the demonstration a learning experience and as interactive as possible. See Figures 4, 5 , 6, 7 below.
It was an honor and a wonderful experience! Thanks to everyone that was able to stop by and say Hi!
It was great to be able to explain the fun and challenge of tessellation design at the MFA.
I am pleased to announce that I have been asked by the Museum of Fine Arts Boston to demonstrate my tessellation techniques in conjunction with the first M. C. Escher exhibit at the museum. My demonstrations will take place in the John, Bertram A. and Ronald M. Druker Family Pavilion (Classroom 159) on February 11, 2018 (Sunday) from 12:00 to 3:00 pm and on February 14, 2018 (Wednesday) from 5:00 to 8:00 pm. The event is free with museum admission. I will be showing how I begin a tessellation and then a watercolor of the design and linocut techniques. Additionally I have some take always for those that want to try their hand at making tessellations! Please come by and visit and see the Master works of M.C. Escher in Gallery 153 and 154 during your visit! For those of you that are Escher fans you must see the exhibit.
To access the artist demonstration calendar and MFA website:
Figures that transform from one geometric state to another are very interesting and elegant. Escher was of course a master at these elaborate constructions. His Development I (Catalog 300, November 1937) is a great example of the chessboard transforming into lizards. The black and white contrast is exemplary and a testament to his graphic skills. Over the years I have attempted several of these types of transformations. The earliest is in Metanoia (1986) which can be seen on my tessellation art gallery page 2. It's a two color lithograph of Icarus materializing out of a more abstract form overlooking a strange landscape. The design for the recent tessellation uses Icarus in a different symmetry family ( IXD4 <Escher> or P4). The image developed from a chessboard design I called Development II (Figure 1 below). This tracing was used for a guide to creating the ink and watercolor drawing of Rise and Fall (2017). I transferred the tracing to watercolor paper and inked it with sepia color ink. Figure 2 below depicts Rise and Fall.
This image uses my horned lizard motif. I decided to create the design after looking at some of my older reference material . The tessellation is a spiral of the horned lizard that slowly transforms to an abstract figure as it marches towards the center of the design. In all there are 450 copies of the motif in the tessellation. The orange, sienna and yellow contrast to enhance the swirling motion. The design was hand drawn and painted with watercolor and ink. I created it by first drawing a sector on tracing paper and then copying it on a light table. Overall the image is similar in concept to some of MC Escher's developments. The design of the swirling pattern was created from one of the design templates in John Willson's book, "Mosaic and Tessellated Patterns and How to Create Them", Dover 0-486-24376. Figure 1 depicts Development I (2017). Figure 2 depicts a detail from the watercolor.
The Centaur's Forest is an image that came from the standing centaur tessellation I mentioned in a previous blog. The image is a simple translation with very little articulation but I decided to develop it into a linocut. Although its not as complicated and articulated as the "The Golden Centaur" image in my earlier blog it seemed easier to include it within a forest. The moon is faintly appearing through the clouds. The tree is a transformed centaur. Figure 1 is a pencil drawing of the concept that became the linocut. I decided to remove the trees in the background as they detracted from the central tree image and that of the contrasting tessellation of the centaurs in the foreground. Figure 2 depicts the final linocut print of "The Centaurs Forest".
Michael Wilson has been creating tessellation art for over 40 years and is preparing this blog to share thoughts on the subject.