It seems like the dragon motif is a popular theme for tessellations. I have completed at least three different forms of dragons that tile the plane and have been working on the enclosed dragon tessellation for a couple of months. Its a new tessellation design in a P3 group (Do3 Polya) and has an interesting motif of a little dragon similar to the dragon figures in my background header. I've chosen to include a template if you want to print it out and color it. I am also including two color variations or versions. Overall I am quite pleased with the outcome; however my ultimate goal is to create an icosahedron with the motif and also a picture story with the dragons running around the page.
I'm not sure if and when I will get around to that as it seems like I get further and further behind with my ideas and the completion of the images than I can possibly complete. Hopefully you will try your hand at making these types of tessellations and even creating an icosahedron. There are many templates for these on the internet. If you choose to make this into a three dimensional figure you will need two of the templates and will need to very accurately cut them out. I have not matched the outlines so will not guarantee they fit together well. One thing is for certain drawing them in two dimensions is difficult enough and the accuracy that is needed for creating a three dimensional object requires even more precision. There are a number of computer generated tessellation programs on the web which may help your quest. I however try to use hand drawn methods and tracing paper. Figure 1 - Dragon P3 Template. Figure 2- Dragons P3 Blue and Green. Figure 3 Dragons P3 Red and Orange.
There are a number of great butterfly tessellations out there. I really like Escher's No. 12 and No. 38 and No. 70 and especially his Circle Limit with Butterflies (1950). Alain Nicolas has an excellent example of a type 2S butterfly motif. I am sure there are many other examples out there as well. The following example is of another butterfly tessellation I created and left in my sketchbook for many years because I was not happy with the design. The Figure 1 below depicts the butterfly motif with two styles that were rejected. As you can see the difference is slight between the tessellation motifs but the sketch allows no overlap and the black and white does not overlap. The problem with this design is that the wings are too narrow in my view. The final design allows overlap and the wings are wider. I chose to include this second design recently within a Mobius strip since it allows the figure to evolve into a colorful butterfly that flies off the page. This concept is similar to several other Mobius strip designs (three other examples are shown on the tessellation-art-gallery pages). Figure 2 depicts the final design of the Butterfly tessellation.
A few people have asked me to provide additional examples of how I develop a print and my thought process. This blog will provide some of the details on the development of "Twilight at Castellano". This image came from one of my sketchbooks and is originally dated January 31, 2013. It has taken me four years to convert in into a print. Its not that I didn't like the image but I have so many ideas and can only execute a portion of them. This idea came from a visit to Italy many years ago and the location is completely from my imagination. I had been thinking about birds flying in formation (ie geese) and the spaces between them. I came upon the idea of doing a tessellation with birds and bats to contrast light and dark. The Figure 1 image was taken from my sketchbook and Figure 2 is a refinement of the image.
I transferred the image to tracing paper and had a lithographic stone prepared by my master printer at Muskat Studios. I choose to make the image a black to white scratch drawing from a black tusche background, It required the use of razor blades and knives to remove the tusche and build the light from the dark background. I started with a completely black background and scraped away at the stone to reveal the lighter portions of the image. This was not my first reverse image. I created "Above and Below"(See the Tessellation Art Gallery) through a similar method. Figure 3 depicts the transfer tracing I used to transfer the iron oxide paper image to the stone. Figure 4 depicts the surface of the stone as I removed the tusche. You can see the outline of the iron oxide on the sides of the drawing. Figure 5 depicts the final image on the stone (note: I flipped the image so that you would see it as it would be seen in the final print.)
The following blog will provide two images related to horses and transportation. The first image is an aluminum plate lithograph that has been hand colored. Its an image I created several years ago while taking a printmaking class. I developed the concept thinking about horses and horsepower. I juxtaposed the two images of the automobile and the horse to show how the common mode of transportation has changed over the past 125 years. Figure 1 depicts Horses and Horsepower.
The next image is a recent adaptation in black and white of the motif Horsemen II. The symmetry group is D1gg. I enjoyed creating this image as its very graphic. My favorite images are pure black and white and this is my own take on M.C. Escher's tessellation "Horsemen"(No. 67). The image is more angular and is not as elegant as MCE's but complements my other horsemen image which faces one direction as a D1kk. Figure 2- Horsemen II (2017) and Figure 3- Time Warp with unidirectional horses.
These two tessellations are from the same D4 symmetry group however they differ in that the four color version in Figure 1 has interlocking birds flying in circles. Figure 2 depicts an enlarged version showing the interlocking rotations. The figures are similar to M.C. Escher's No. 118. The "star" comes from the eight birds that surround a central point (four heads, four tails)and the D4 overlaps. The second tessellation or tiling is black and white. I have taken the same symmetry group and combined a jet and a bird motif. These two images look very different but are very much related.
I am attaching three folio sketches to this blog. The first depicts a sting ray motif that is able to be tiled in two symmetry groups. The second is a lizard tiling that is a variant of the tiling I used on the print "One World". They are all three related by their symmetry groups. The lizard tiling can be tiled as a D1 gg or D2 kgkg with a slight variation. Its fascinating seeing some of these tiles that are able to tile the plane in two ways with the same motif.
The following post will include an example of a spiral tessellation. I am unaware of any symmetry groups that describe spirals. This tessellation is based on a P1 tile of an owl. I have called it an S1 symmetry group. Figure 1 depicts a double spiral tessellation of the owl motif. Figure 2 depicts a page from my sketchbook of the original idea. This is translation and I choose the double as it seemed more interesting than a single spiral. This design is similar to the lizard in my print "One World" since it covers the sphere in a spiral. I am researching some ideas into multiple motif spirals and different ways to combine them.
There are a number of life-like single tile tessellations that have multiple motifs. This blog describes a tile that has three different motifs, two bird designs and one fish design. Multiple motifs are not common but there are a number of them that have been created. These three motifs are not unlike some other dual or multiple designs on one tile. This tile is a P4; very similar to Polya's D4o plane symmetry group. Creating dual and multiple motifs is not something that I normally do however this image is very recent. Figure 1 below depicts the concept as I developed it in one of my sketchbooks. Figure 2 depicts a more formal color version of the tessellation. For those that want a challenge try creating a multiple motif tessellation. Its fun and when the motifs are mixed together it becomes complex .
The following describes the process and development for this image. A long time ago and I hate to admit this but in 2001 I created the layout for this image. In fact this was one of the first images I sent to Andrew Crompton for his website People Doing Tessellations. So I dated it and drew this on tracing paper and then put it away in one of my portfolio notebooks. Well I had always wanted to make this a color drawing. I finally decided that I would finish it. Why it took me so long I do not know. Its possible that I remembered the image of the barn and had just completed Almost Extinct earlier this month. So there are two images and tessellations that include barns! The Figure 1 depicts the original image from 2001. Figure 2 depicts the colorized version with a few changes or edits.
I have many unfinished projects. I hope to be able to continue to complete the old ones and also generate some new tessellations to incorporate into my artwork. This blog gives me a way to convey my ideas and hopefully inspire others into trying their hand at creating tessellation patterns. I know that my work normally tells a picture story. That's not to say that the pure form of creating tessellations is not valuable. It is very valuable and very interesting especially the beautiful work we can see from many websites dedicated to this artform.
The tessellation and drawing in the figure below depicts two types of dinosaurs and a small farm. Just as the dinosaurs are extinct the small family owned farm is slowly becoming extinct. The tessellations are of a tyrannosaurus and a triceratops meeting each other on the page. I believe they are both C1 types of tessellations. The barn is similar to many barns I saw growing up in the Midwest. Many of them are now falling down or need serious repair. When you see these barns many times their roofs are collapsing or they are leaning and you can see the purlins or other parts of the structural "bones" that have been exposed by time. They remind me of the dinosaur bones unearthed by archeologists. The sun is setting in the background and shadows are forming. Hopefully time will not set on the small family farm.
Most artists have two or three images they work on at the same time. I typically have two or more in development and many tessellations that haven't been previously used. This drawing is based on a tessellation I completed a number of years ago after I did a quick sketch in one of my sketchbooks. Its probably been in the sketchbook for a couple of years, I'm not really sure. This "tessellation shape" was used for another lithograph I completed many years ago called "George". Gorilla Business was created from that same basic shape but I changed the image somewhat and I finally got around to making the drawing. Its based on one of the simplest of the 17 types of tessellations(D1kk). Hope you like it.
All of my drawings are originally developed on tracing paper. The reason is I can't draw that accurately and need to have the repeating tessellation copied many times so it requires a good amount of repetition of the base image which need to stay in proportion. The final image of "Gorilla Business" is the figure below.
This blog will be dedicated to two examples of transformations with symmetrical isohedral tilings or tessellations. Polya describes 17 groups that tessellate the plane and Geoffery Shepard in Structural Topology 15 (1988) describes 93 isohedral patterns and groupings for coloring tiles. My goal is to show how a symmetrical isohedral tiling can be easily transformed from one design to another. Figure 1 below depicts Jets & Pterodactlys in the same shape that is a mirror image of each tile crossing the design. The pterodactyls go right to left and the jets from left to right. If you are able to create a design with a same shape and it tessellates the plane it just takes some creativity to transform it into another recognizable figure.
Figure 2 depicts a different type of tessellation that is a p4 rotation. The bird and the fish tiling is excatly the same shape but rotates 90 degrees to tile the plane.
My first attempt at making a tessellation occurred 38 years ago. It was an attempt in that I didn't understand how tessellations worked or anything about their properties. It was pretty much a failure and involved a Jets and Pterodactyls motif. It grew from a short discussion I read in The Magic Mirror of M.C. Escher (1976) by Bruno Ernst. I had just gotten that book as a birthday present in 1977. Figure 1 depicts that first attempt.
Figure 2 was completed just a few days ago and is the same design motif but I think represents one of my better designs. Again the subject matter is Jets & Pterodactyls in a D2kkkk pattern. I have several designs with this motif but they are all different tessellation patterns. Figure 3 Past and Present depicts another example of this motif as does the Figures 4 and 5. I guess you can say I've come full circle and created a cycle with this motif. Hopefully you will create a motif with different tessellating patterns. It sometimes takes me years of doodling in sketch books to come back and revisit earlier designs-so everything old is new again!
This blog will describe the method of creating a stone lithograph and depict the image making or drawing process on the stone. I have prepared stone for printing and processed hand pulled stone lithographs in the past I normally use the services of a master lithographer for the processing and printing. I have been working closely with Muskat Studios and Carolyn Muskat for several years. She has great local litho studio so I leave the printing process to her and I concentrate on the image making. color selection and design.
The first step in any artwork is to decide on the size of the print and the color scheme. I choose a stone of the proper size which is typically 4- 5 inches more in length and width than the image to allow for paper and margins. While I have done color lithographs I prefer the pure values of black and white and its simpler than color processing. I have always liked black and white and that is probably why I have been attracted to lithography in the first place because you can achieve an immense variation and gradation on the stone and there is just something cool about drawing on a rock! So this blog will provide a depiction of the image making process and the buildup of values. I am going to make a bold statement- "Drawing on a Lithographic stone is hard. Painting is easy compared to drawing and applying values to a litho stone". If you can draw on a litho stone you can paint. (I expect to get some feedback on this and everyone is entitled to an opinion.)
The first step is drawing. Creating an image that will be something you want to make copies of in a print format. Figure 1 is the initial drawing on tracing paper for The Artist's Dream.
Once the tracing is complete it is transferred to the stone with iron oxide paper. You place the iron oxide paper over the stone and then the tracing paper over the top of that. You then use a pencil and go over the lines and transfer them to the stone.
Figure 2 depicts the initial transfer of the lines into the stone.
The first thing you will notice is that the image on the stone is a mirror reflection of the drawing. This is important because anything that is drawn on the stone including lettering and numbers such as shown on the ruler will have to be a mirror reflection of what is in the final print. It can get somewhat frustrating if you are not used to writing backwards. The line drawing is red in color due to the use of iron oxide. Iron oxide does not reproduce when the stone is etched to make the lithograph but allows ability to re-draw the image on the stone.
I use various grades of grease pencil. Grease attracts grease and water repels grease which is the primary chemical process in lithography. The grease pencils have to be very sharp when you begin the drawing process. It usually requires a sanding pad to sharpen the pencils. So every lithograph that I make requires drawing the image at least twice! Its not as simple as a sketch or a drawing since you need to think through color and the way the image will look in the final.
Figure 3 and Figure 4 depict the development of the drawing on the stone. Figure 4 shows the final image prior to processing the print.
Note that Figure 4 shows the reverse lettering on the eraser and the ruler.
The master printer develops a number of proofs based on the values and gradation of the drawing. I work with the master printer to choose the paper and the number of ink passes to create the correct balance and density for the image and the prints. Each print to compared to the approved proof to determine whether its acceptable for inclusion in the edition.
The final print of the The Artist's Dream, 10" x7", edition of 25.
This blog shows two examples of the translation of 60 degree rotational (P3) tessellations to 90 degree (P4) tessellations. Many symmetrical tessellation designs, that is a tessellation with mirror reflection about a central axis, are capable of being transformed from the 60 degree (P3) state to a 90 degree ( P4) form. This doesn't mean that the design will be able to be simply copied just that a form of the design can be modified from one state to another. I thought I would show a couple examples of how this works and provide some commentary on the modifications.
Figure 1 depicts Horned Lizards as a 60 degree rotational design or a P3. The tessellation is rotated 60 degrees and repeated. Figure 2 depicts Horned Lizards as a 90 degree mirror reflection design or a P4. The design repeats at 90 degrees as a mirror refection. Figure 3 shows Jets and Pterodactyls as a 60 degree rotational design or a P3. Figure 4 is a 90 degree reflection of the same design.
There are many symmetrical tessellations that can manipulated in this way. Normally the approach I take is to start with a P3 (60 degree) design and overlay a it on a square grid with tracing paper. I then stretch and create a 90 degree grid with "mirror symmetry" and design around the center axis to complete the tessellation.
The following is an example of how I create tessellation art. I typically start with drawings in a sketchbook similar to the Figure 1. Many times these designs sit for months and even years before becoming a print or drawing.
Figure 1 depicts a tessellation titled "Bats & Birds" from one of my sketchbooks from December 2000! Not all designs take this long from creation to development but this one was definitely longer than most. A portion of this tessellation design was used in creating the image for "The Lost Domain". However there are typically two or three steps in development. First the tessellation has to sized and repeated. Following this step the image needs to be combined with a theme, idea, story or figure and ground within the art.
The image for the Lost Domain had at least one theme that was rejected. Figure 2 below depicts the rejected theme.
My thoughts about the direction of the image changed somewhat during the development. After rejecting the Figure 2 design I recalled a book I had read many years ago entitled "The Wanderer" also called "Le Grand Meaulness(The Lost Domain) ". The book was written by Henri Alain-Fournier in 1913. Unfortunately he was killed in action during World War I. The final image was created from my interpretation of the book. Figure 3 depicts the final version of the image.
Its not unusual for many of my designs go through several iterations before they are finalized.
The final image for The Lost Domain, August 2016. By Michael Wilson.
Michael Wilson has been creating tessellation art for over 40 years and is preparing this blog to share thoughts on the subject.