A colored pencil and graphite sketch of a jet plane and dove tessellation. Figure and ground; a simple translation. Drawn on Twinrocker paper. Its a small drawing about 6.5 by 6.5 inches. Thought it was appropriate based on recent events.  The thing is you can't have the one without the other in the world of tessellations; they co-exist. 

This is a motif with elephants. It's a glide reflection. This was done in watercolor with the original pencil sketch below. I also have a much more linear elephant motif I completed as a linocut several years ago. That motif is located on my art gallery web pages. 

An image of a sabertooth tiger as a P3 rotation. The watercolor image and original pencil drawing are below. 

The image below is a motif of Lady Godiva. I got the idea after seeing a box of Godiva chocolates but the image is mine. Then much later I realized that the late John Osborne also did a motif in a different position. His image can be seen on the ozbird.net webpage. The below is a watercolor and pencil image and the pencil sketch. Its a pure translation. The simplest tessellation family. Those Godiva Chocolates are wonderful! 

Arguably the most common Escher print seen on the internet is Angels and Devils. There are many different tessellations with the same theme. I've always admired Eschers Hyperbolic Tessellations and in particular Angels and Devils. My interpretation is a simple translation which is depicted below. I've also done a pencil sketch study for a circle limit or mandala with another version of my motif. I may use the circle limit image on a future lithograph.  Angels and Devils with watercolor on paper November 2020. . 

The image below is a newly created stone lithograph I recently completed based on the farthest identified single object in the universe. Astronomer's discovered it using a new technique called gravitational lensing. The blue super giant star is 14 billion light years away and was named Icarus. Its official name is MAPCS J1149 Lensed Star 1.  Its hard to think about such a vast distance it's simply incomprehensible. In fact the star no longer exists only the light that was emitted from it billions of years ago. So when you look into the night sky ask yourself who is the time traveler you or the stars you see twinkling!

​The print was made as a stone lithograph with four passes through the printing press. Carolyn Muskat of Muskat Studios printed the edition of ten. The background was made from a Lo-Shu wash that was turned and printed three times. Finally the tessellation image was printed over the background. 

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,
Transformed utterly:
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. 
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​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. 
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