Einstein Hat Awards (entries 187-160)

Thank you to our sponsors, XTX Markets, UK Maths Trust, National Museum of Mathematics (MoMath.org), Amplify, G-Research, Jane Street and Dexter and Deborah Senft.

Contributors - Geoff Smith, Simon Coyle, Samuel Monnier, Dianne Flatt, Cindy Lawrence, Chaim Goodman-Strauss, Guillermo Acevedo, Kit Reagan, Hayley Richardson, Philipp Legner, Craig Kaplan, Robert Fathauer, Yoshiaki Araki, Dexter Senft, David Smith and Ewart Shaw.

187 Konda Luckau 50 USA

Name: Turtle Garden

Size: 59" x 74"

Medium: Cotton Fabric

As an avid quilter, I decided to make a quilt to celebrate the discovery of the hat. I decided to use the turtle variation for the quilt because the designs resembles a hexagon. The hexagon is a common, although challenging, shape used in quilt making. The most common setting is called the grandmothers flower garden. I used this setting as a starting place for my quilt. The orange turtles are the center of the "flowers" and are also the turtles that are mirrored. As the turtles tile in a non-repeating pattern unlike hexagons, I added extra turtles into the setting. The black and white turtles are the extra turtles. Because the turtle is a concave polygon, the pieces were very challenging to piece together using traditional quilting methods. It would have been simple to piece had I broken the turtle down into equilateral triangles, but I decided to take on the challenge to preserve the integrity of the turtle shape. To complete the design, I quilted the quilt with a stitching pattern I designed that is numbers.

186 Esteban Ponguillo 25 Ecuador

My entry refers to a system for coral restoration using the Hat Tile.

The first image is a view of the individual tile, in the interior of the piece a hole (1) has been introduced to reduce drag both during the transportation and installation of the piece as well as to facilitate marine fauna to live inside such as morays and eels. This hole also allows the formation of diverse cavities, caves and crevices that are characteristic of natural coral reefs, this increase the interior surface area of the artificial reef making more room to coral colonization.

The upper half of the hat tile has 5 pyramidal slots (2) that fits with the lower half spikes (3), this allows stacking creating multiple stages (will be seen in the second image). The slots also allow for the connection of small coral nurseries (5) with its respective coral explant on the top (A)(4).

In the second image we can see the full system in action featuring 3 stages, each one with fewer hat tiles than the previous one, the upper view reveals that even with multiple stages/floors, the ocean floor/base is still visible (B) allowing for more sunlight to enter. A frontal views reveals that the stacking of the hat tiles has multiple holes (C), this allow for water movement across de complete system reducing drag, and the chance of knocking down of tile due to currents also improves the total lateral surface area. The last view lets us see the staircase (D) that is formed by multiple stages showing the multiple floors of the system.

This system allows for overhangs, arcs and other features that improves marine life interactions and niche formations. And because this kind of tiles never repeat itself and its infinite, means that every new configuration will be new and the reef can be expanded as desired, just like a real life form, this will most likely improve adaptation and a proper artificial ecosystem for all kind of marine life, not only corals.

The introduction of multiple stages as mentioned before allows for various formations that promotes marine life to live there, but also means that the tiles work as construction blocks having endless possibilities about what you can make and design based of the necessities of your local reefs.

Thank you for taking the time of reading my entry. 

185 Evan Badcock 15 UK

This is Einstein's face created from 'Einstein's Hat Tile' biscuits.

First of all I 3D printed the shape of the hat cookie cutter using my 3D printer and a file I found on the internet.

I then found a recipe for a biscuit dough that would not spread when baked and then made the dough and cut out around 70 biscuits and baked them.

Next I used colour to highlight Einstein's face on an image of the tessellating shape taking inspiration from the famous picture of Einstein with his tongue sticking out. Once my biscuits were baked, and I had researched how to colour entire biscuits, I created 4 different colours for the hair, nose, tongue and eyes and applied them accordingly. After all the biscuits had been coloured I arranged them into shape copying my design giving the final picture of Einstein's face.

184 Ilora Nandi Ball 15 UK

Hi, I'm Ilora and I'm home-educated. I'm 15 years old and live in the UK. I would be in year 11 if I was in school here. I've always found geometry and tessellation so beautiful and interesting, and it's definitely something I'd love to study when I'm older.

I recently started teaching myself how to use blender, a 3d modelling software, and this was a great opportunity to experiment with this amazing new tile!

I tried to make a small cityscape in the form of a floating island made from hat tiles. It took me a while to get the shape of the tile exactly right so it would tesselate without any gaps, but I'm glad I persisted as I feel like i have a much deeper understanding of all the incredible stuff going on within it! I made it by tessellating about a dozen tiles and then extruding the ones around the edges to make buildings.

I think it turned out quite interesting and I'll definitely be expanding on this in my own time.

Thank you!

183 Claire Boardman 38 UK

I'm a Maths teacher and wanted to get some pronoun badges made to wear on my lanyard for school. For the background I chose the newly released Einstein tile and am thrilled to have something subtly geeky. I run the Pride Society in my school and teach a number of trans and non-binary students so I understand the importance of visibility and of treating people with the respect they deserve. I want to help usualise the practice of pronoun badges and asking pronouns, but they're sometimes difficult or expensive to find so I had to print my own.

182 Jessica Sklar 49 USA

Our 18" × 22.4" pop art homage, "Monotile Quadriptych," reminiscent of Andy Warhol’s prints of Marilyn Monroe, celebrates the hat monotile with bright colors and a mischievous cat, wedding the abstract to the everyday.

181 Henry Manning 16 UK

I carved a jack-o'-lantern using only the hat Tile for its eyes mouth, in the spirit of Halloween.

178 Adam Rowe 46 USA

At one end of the spectrum containing aperiodic monotiles is a shape which can fit copies of itself to form a hexagon. (This shape is represented by the red, green, and blue color fields in the flat painting and half of the sides of the sculpture.) This arrangement of the shape copies also represents a group of three rectangular solids seen with minimal parallax distortion (or abstractly, in a isometric world).

177 James Westphal 23 Australia

The following brief essay and concept photos are a culmination of over half a decade of imagination and two months of practical application and 3d engineering to create a brand-new board game.

To Summarize what has been expanded upon below, I have created a new board game named Aurellian (at the moment), using the Einstein shape as the main building block for the mechanics, engineering and overall look and feel of the game. After five years of imagining what this game could be, this new discovery has really changed the course of my life. From the overall aesthetic of the shape, to its practical application, I have tried over twenty shapes to no prevail, all until the brilliance of David Smith and his hobby. I have attached two photos below that show case my creation the best. Below is an essay surrounding my journey with the shape over the past five years with brief descriptions on how the pieces in the first and second photos work.

In 2016, during a family holiday in China, I embarked on a creative endeavor that would meld my love for the widely popular games of ‘Age of Empires’ and ‘Settlers of Catan’, into a new unique board game, entirely of my own making. Nicknamed ‘Aurellian – the Black Water Rebellion’.

Drawing inspiration from these beloved games, that gave me such escape as a child, I sketched out the first foundations of Aurellian, determined to craft an experience that would resonate with likeminded individuals who share my love and enthusiasm for such strategic gameplay set within a medieval theme.

Using hexagons to tile my plane I set to distinguish Aurellian apart from Catan, who tiled their game with the same shape. By dividing each hexagon tile into six equal kite shapes, the finalized versions seen below, I was able to create a fresh design that allowed for me to place two different sized road pieces (Seen as white strips in photo one and number 10), along with six new resource tiles that created a new unique look from Catan and other similar board games. However, even when marked with new iterations and designs, the image of a hexagon still belonged to Catan. Furthermore, singling myself to a hexagon as my games design would have fundamentally changed the way I would wish to play my own game.

Therefore, the journey to create or find a new shape that incorporated the following; listed below, took place over the next five years.

Aurellian’s Tiles must:

- Be a new uniquely shaped shape that other games have not claimed or developed upon,

- Be iconic and easily recognizable,

- Be a shape that can be tiled infinitely on one flat plane, but also able to be manipulated into breaking away into new multiple planes that cannot connect to one another if originally continued,

- Allow for multiple evenly equaled kite shapes that make plotted hexagons when placed bare,

- Present the players with naturally looking kingdom walls for a more aesthetic look,

- Be a shape that can be easily manipulated into new fundamental pieces, i.e., water tiles, new main tiles, Kingdom walls, etc,

- Allow for a static board game image that can also be broken up into a more naturally flowing look,

- And most importantly, must allow the player more range and control over where they place their kingdom.

However, fast forward to September the 1st 2023, where I was scrolling on a reddit math’s forum, I was lucky enough to stumble upon a post outlining the breakthrough of the Einstein shape, found early this year.

Instantly, I realized that this shape was everything that I had been searching for, mathematical, design and aesthetic wise.

So after downloading a free trial of a 3d printing program, and dusting off my brothers 3d printer, I began to teach myself a way to engineer the Einstein shape into my board game idea.

Before then I had tried to reorganize almost every shape under the sun into working with my game.

Even trying to engineer the new spectre shape into working with my envisioned design, yet I came to no prevail.

However, after only a few days of learning, I was able to create my first design of the Einstein shape and print it off the next day.

Below is attached two photos of my board game, which includes over 350 individual pieces that took over 120 hours to print during the month of October.

It is also fun to note that when I began creating Aurellian around the Einstein shape, I was unaware of the Hat contest. It was six days in when my brother, the one with the 3d printer, came across the hat competition, sent me the link and encouraged me to apply. So beyond all else, i feel as though these past five years have some what led to this moment. Some poetry is too perfect not to sing.

Anyways, enough of that, back to what I was saying. With the Einstein shape, unlike all other shapes, I am able to create a naturally looking kingdom that houses tiny 3d printed city pieces. These ‘kingdom walls’ (Number 1), as I call them, are seen in the first and second photo. Photo one you can see four of these Kingdom walls, each able to be placed anywhere on the map, rotated in any of the six directions, and can also be flipped over so that its reversing face can allow players to reach more tiles. I wont go into the specifics of how the game works to save time, however I will point out that where a player begins at the start of the game is important and can determine what resources that player will receive upon a dice roll or the beginning of their turn.

The Einstein shape in these regards is crucial, and allows the Kingdom to appear somewhat naturally, whilst also allowing the Einstein shape to be placed onto of another Einstein shape.

I know this may sound confusing over text writing, so the second photo is able to give us a better view and understanding into how the Einstein shape allows this game to be played, rather than using any other shape.

In the second photo you will see numbers assigned to various groups of 3d printed models. I will be referring to their number correlation to try and translate the mechanics and engineering of the game.

The Einstein shape labelled with the number 1, is the Kingdom walls.

At the beginning of the game the board will be set, seen in photo one, and each player will place their Kingdom over the resources they wish to gain, as stated previously.

Number 2 shows us the main Tile that the entire board is made up of. Each Einstein tile, as we now know, can be infinitely tiled across a plane, if added with a few of its own reflections. Number 2 will be placed down first in any way ones imagination sees fit, allowing them to make more intricate maps then what other tiling shapes can allow. This is an advantage that I needed to have, as I enjoy playing games upon intricate and highly detailed maps. An important advantage of the Einstein shape. Number 3 shows you how I have printed the main Einstein tile and its reflection, and how number 1 is able to be flipped and be placed on top of the two different tiles with ease. This means that although I may have to print two different types of tiles (The main and its reflection), I only need to print number 1 the same way every time. If you also glance at number 4, I have showcased how the Einstein wall tile (number 1) is able to be placed so differently across the main tile, (Number 2). Allowing players greater freedom of placement, not given by any other shape.

Now if we have a look at number 6, it is a little hard to see, however I have been able to print the main tile and its reverse and stick them together. The main reason why number 6 is hollow, is to reduce plastic consumption and see if the structural integrity holds firm. Side note, it does. If number 6 could easily be produced, this would mean that when setting up the board, players would be able to easily create the board by either using the normal face or its reverse, as to continue the plane. Flipping one main tile rather then differentiating between the two.

Number 5 is to show that it is possible to split the main face and its reverse face and have them click together. This would allow for the board to be held together from underneath. Another advantage of the Einstein shape that I have not found in any other.

Number 7 is a show case of what I mean by resources. These smaller tiles (Currently upside down), fall within the kite shapes of number 2, allowing the players to fill the board with color and resources to fight for and capture. The main kite pieces work a treat, however after many attempts I found a problem with only using the one tiles (Number 7).

Also, at this time I will take a breath and explain my overall goal for the mechanics, aesthetic and feel of the game. I will also take this time to either apologize or congratulate you on keeping up with or falling into a rereading mess of confusion, for what I have just put you through.

The main mechanic of this game is that I want to have a board that can be either infinitely planed or be broken up into multiple different planes that may not mathematically work on paper, yet can still be travelled back and forth using the water tiles. How I have achieved this, is that number 8 (Face down) and number 9 (Face up) are my water tiles. These blue tiles are able to be connected to the main tile planes and extend them further or extend them pass their current planes mathematical ability. By adding a new layer on top of the current number 2 plane, when creating a new map, players are now unrestrained by the Einstein shapes mathematical abilities.

Say per instance that you are only left with reverse facing tile number 2’s, and you want to make a new island only using them and a few normal face up tiles. You can now extend the water out past the current planes ability to do so, and begin a new island. In number 8 you will be able to see the three brown pieces. Two are able to connect water tiles together, and the third single one is able to rebalance any edges that may be slumping. An advantage of having an equal kite shaped block as the main mechanic of number 2, that makes the Einstein shape whole.

Another main focus that I have for the game is that it must feel like a board game, whether it be through straights and edges, but also has a natural environment feel on top of it. And what I mean by this is that if you look at number 7, you will see double resource tiles below the single tiles. One problem I was faced with was that by only using single-colored tiles, the game felt like a generic board game with visible hexagons after hexagons that stood out in a repeating pattern. However, thanks to the shape of the Einstein shape, and the unique kite shaped inlays, the double resource tiles not only hold the bord together for added security, but break up the hexagonal patterns that stick out to the human eye. Making it much more pleasant and enjoyable to look upon. Before the board looked extremely childish and repetitive, however now, as seen in picture one, the board is now able to be broken up into more naturally flowing shapes and patterns, whilst still having that hexagon feel. This is important to me, especially when it comes to enjoyment, playability and remembering where I first started. Sadly however, my brothers 3d printer is not small enough to create scenery. So, to counteract this, you will just have to imagine multiple farms, villages, greenery, environmental and smaller scenery, scattered across the map.

On top of image one, you will see multiple brown pieces, either shaped as boats or medieval units (Also seen on number 10). These will be moveable pieces that allow players to attack each other’s kingdoms, set ablaze to their farms, lay siege to their kin or create trade blockades on their roads and water ways.

Another product of the game will be the cards that players will constantly be drawing and trading. On the back of these cards will have the Einstein pattern so that players can randomly lay the cards face down on a table and a map will be formed for them to build upon. This is another advantage that I feel as though would be diminished by any other shape.

For added transparency, most of the prize money won will go towards investing in stocks, as this is what I do for a living. 10% will be donated to the royal children’s hospital Melbourne, and the rest will be spent on a better 3d printer. In a few years I wish to have enough money to create my own franchise in the sci fi fantasy space, with Aurellian being my first project, and my book series and tv shows being my second and third.

In conclusion I thank you for giving me and others alike an opportunity to showcase our creativity. I thankyou for reading and viewing what I have to show you and what i have worked on for the past month. I hope you enjoy and feel free to contact me if I need to explain anything more cohesively or expertly.

176 Noella Wamala 17 Uganda

Both my second and my first file constitute specific art and and design pieces I created using very different tactics but similar characteristics.

One is of a painting of a black woman peacefully sitting in what one would call a natural environment, untainted by humanity's desire to change what already exists into something else. Her calm demeanour suggests that she is exactly where she is supposed to be and all is right with the world. When I placed the lady in the centre of my painting, I intended to acquire a perfect image of the world around her while making her the centre of it all too, Of course I had to fight hard ton make sure that I maintained the natural symmetry of the painting all while playing with a few asymmetrical features in some of the details for example the stars and birds that appear in the distance. Shapes were also very important in this painting whereby my main focus was on the use of circles and a semi circular mode of painting in order to create a specific emphasis on where the viewer's eye should mostly focus on (the lady). Creating a 50% balance between the sky and the land also helped me maintain the geometrical symmetry of my painting.

The second file, consists of two identical cargo pants that I personally designed, as you can observe, the pants posses many designs that are intricately yet symmetrically placed. The designs consist of both regular and irregular shapes that work together to bring out the design of the pants all together. The time and effort in took to delicately measure and cut each part of the pants helped me bring out the final piece and I might as well say, I am very proud of my two pieces and I have learnt to appreciate the mathematical procedures of measurement that I had to apply into these pieces in order to attain my final pieces.

175 Kenise Gaston 23 USA

The Hat Maze Puzzle

The goal of this puzzle is to successfully arrange the monotiles within their correct, fixed space by sliding and rotating them on their wires. Each side (black and white) requires a different pattern arrangement to solve.

Based on the classic bead maze toys, this design also becomes a toy for younger children that exercises motor skills and spatial reasoning.

174 Valerio Pellegrini 56 UK

The assembled work comprises an 80cm x 60cm background on which are placed spectre shaped tiles that have been created from a coated acrylic sheet, 3mm thick, laser cut to within 0.2mm. There is a number of different finishes which have been used:

– Painted finish in two-pack polyurethane top coated with two-pack acrylic lacquer 2% dead Matt

– Rugging effect in white pearl top coated with two-pack acrylic gloss lacquer and polished

– Copper and brass Liquid Metal raw finish spray applied (textured feel and look)

– Copper and brass Liquid Metal with blue/green patina applied, top coated with two-pack acrylic gloss lacquer and polished

"Journey to Infinity" is a representation of the infinite universe. The mathematically defined structure and the aperiodic nature of this amazing shape easily leading the viewer towards infinity through an unending series of patterns.

The tiles and their coverings represent the building blocks of matter, atoms, protons, electrons and sub-nuclear particles bound together to form a representation of stars, galaxies and celestial bodies

To enhance the visual appeal, a variety of materials and different techniques were used. The materials include pearlized paints, powdered metal, resin and pigments in various colors. The pearlized paints add a shimmering effect, giving the illusion of distant stars. The blue on black effect gives the impression of swirling clouds of cosmic dust within deep space.

The work is also the result of various application techniques used in the coatings which contribute to its overall appearance. Techniques such as airbrushing, ragging and splattering are employed to create a dynamic and organic feel. These techniques emulate the concept of cosmic expansion and movement.

Overall, the objective is to create the impression of the unending vastness of the universe in all its complexity and beauty.

173 Edward Walker 30 Australia

I have designed a set of Hat-shaped "geomorphs" (first image, PDF), for use to create dungeon maps for Dungeons and Dragons and similar tabletop RPGs. Each geomorph tile shows a small piece of a map. By fitting them together, players can generate a variety of large dungeons, quickly and easily [1].

Because of the Hat tiling's large-scale structure, these dungeons have a navigational hierarchy (second image, PNG). Short "suburban" tunnels (white) are common but twist and turn in hard-to-navigate ways. Major canals (blue), are like arterial roads, running straight and true for long distances. The canals are harder to reach, but much more useful to adventurers (and monsters!) trying to cross the dungeon quickly, giving players a navigational choice [2].

This canal network is built on the Hat tiling's structure: specifically, the chains of stacked Hats that link reflected tiles.

While the Hat itself is a monotile, my geomorph set has distinct flipped and un-flipped geomorphs. The un-flipped ones all have the same blue stripe, which lines up to run along stacked Hat chains (if a tile isn't part of a chain the blue stripe doesn't connect and is ignored). On these tiles the blue stripe never connects to the white tunnels, so canal-farers can travel in peace [3].

The flipped geomorphs have "dock" areas that link tunnels and canals together, letting adventurers and monsters move between the two networks. Being flipped, though, they will only fit in the H1 position in the Hat tiling, where the chains meet — and therefore the "dock" areas only show up where they can link up to long canals.

My submission consists of the geomorphs and images as described, which are my own original work.

For ease of visualisation, I have also modified a version of Craig S. Kaplan's "hatviz" app to render maps using these geomorphs (following the terms of the BSD 3-clause open-source license he's released it under). This code is available at https[ :// ]github.com/isikyus/hat-geomorphs, and I've put the modified app online at at https[ :// ]www.isikyus.com/hat-geomorphs/

However, as it's a derivative work, this app and code are not part of my competition entry.

172 Vaishahan Pirapakaran 16 UK

The idea I thought of for The Einstein Mad Hat was a football shirt with a black background and the Mad Hat shape to have a different colour on the front of the football shirt. Each colour means the shape's rotation to make it different from our line so it is different. For the side of the football shirt, I thought of a line from the collar to the sleeve cuff, with the cuff of the sleeves to have a half circle using the mad hat shape with the colour of white sleeves and black shape. I kept the collar plain white as the pattern won’t fit in the collar and it wouldn’t be nice to keep a similar pattern of the collar and sleeves cuff. The whole point of doing this is to show that there are different shapes to be used in a football shirt and it doesn’t need to be the same all the time.

171 Daniel Scott  42 Australia

The attached 3 page PDF contains the backstory and rules to a game I have created called Maadth, inspired by the Hat, for the Einstein Mad Hat Competition.

170 Stan Matthijs 26 Belgium

I programmed my own implementation of the hat-algorithm in C# and visualized the tiled plane in a video game project I've been wanting to make. I tried to be as thourough as possible in documenting my approach and providing the context around procedural generation in video games. I am a junior programmer by profession and work at the IT department of a hospital in Ghent, Belgium. My colleagues declared me a little crazy when I enthousiastically told them my vision for the project. This was by far the most ambitious side project I've ever undertaken. I had no prior experience with any game engines up to this point and needed to learn the basics QUICK. As any programmer can attest to, solving a hard problem like this one just beyond your initial capabilities is an amazing feeling. So I hope you enjoy the read! I'm also extremely curious with regard to the other entries my competitors have come up with. English isn't my native language so I apologize for any errors you might find.

169 Steffi Hudson 43 UK

The tiling was produced from circles as I wanted to created the hexagons from scratch. I do not mind technology but love the use of compasses. This was I could not only construct the tiles but use them in my design. Then I used watercolours, thread and paint to finish of my picture.

Thank you for the inspiration.

168 Makoto Nakamura 76 Japan

Nine sea turtles

・Puzzle where you fit 9 pieces into a frame

・The frame is made of MDF and steel plates and the pieces are made of resin clay and magnets.

・There is more than one solution.

Geometric shapes hidden in nature

・Illustration intended for an exhibition banner

・Software used Adobe illustrator

167 Yang Cao 46 USA

This is a hat design with Einstein hat tile shapes, and it is also a dynamic maze. The maze is based on my invention “Space maze puzzle with reconfigurable paths” (US Patent Number 10780341).

In this particular maze, there are 7 rotatable faces: Top Hexagon (Face T) and 6 Square faces on the side (Face A-F). Each face can rotate around its center freely. Picture 2 shows the complete map and the numbers of each channel position (on each edge, there are 13 positions numbered from 1 to 13 clockwise distributed evenly along the edge). The goal is to move an object from the start point (A1) to the end point (A12). When two adjacent edges have two position numbers adding up to 14, then the two channels are connected and the object can be moved from one face to the other. For example, A1 can be connected with B13 by rotation.

The solution for this particular maze is:

‘A1’, 'B13', 'T1', 'C13', 'B1', 'B4', 'T10', 'T4', 'F10', 'F8', 'T6', 'E8', 'F6', 'F3', 'E11', 'E9', 'T5', 'C9', 'C7', 'D7', 'E7', 'E2', 'D12', 'T2', 'A12', in this order.

The math behind this maze is Dijkstra's algorithm and it is even more complicated than the regular Dijkstra's algorithm since this is a dynamic map. Each time a face is rotated, the map changes. We have a computer program to design and solve this type of dynamic mazes.

Thank you for your consideration.

166 Tricia Horn 41 USA

This submission demonstrates the connection between mathematics and baking with a home baked Rice Krispy treat rendition of the Hat and Spectre tiles. Baking in its precision of measurement embodies mathematics in the process itself, while also providing a creative outlet as in the rendition of the Hat and Spectre tiles. This rendition is composed of 21 gluten free Rice Krispy treats each measuring 5 inches in length by 3.5 inches in width by 1 inch in height with vegan frosting in the same shade as the hand cut fondant shaped tiles that top each treat in shades of light blue, dark blue, white and gray. This rendition is easy to make and fun for both adults and children alike, providing edible pieces that form together to make the Hat and Spectre tiles.

162 Louise Carter 33 Australia

Made from glass beads and thread using a peyote and herringbone combination stitch.

The angles are exactly perfect causing a slight rise where the three flat edges of the kites join.

161 Alec Dixon 61 UK

Spinosaurus aegyptiacus tessellations

Photograph 1: Watercolour and pencil (painted area 67.5cmx46cm) Saunders Waterford

Photograph 2: Watercolour and fineliner pen (painted area 50cmx36.5cm) Saunders Waterford (High White)

I have a long standing obsession with creating tessellations of dinosaurs and other long extinct creatures, so it was only natural for me to see 'The Hat' as some sort of dinosaur hunting ingenuity challenge. ('Pulling a dinosaur out of a hat', you might say...)

My first success was to eke out a rather chunky looking Dimetrodon ( - a pelycosaur, not a dinosaur!). Despite the creature looking rather stiff and angular - and being somewhat lacking in anatomical accuracy - it was still recognisable as a Dimetrodon. I was quite pleased with this early find. Nevertheless, I decided to continue searching...

Over time 'The Hat' shape started to suggest to me the 'M'-shaped sail of a Spinosaurus, as reconstructed by Ibrahim et al. (2020). I was determined to try to nail one down! Eventually, after a lot of wrestling with details, I unearthed these two slightly different specimens. Despite working within the constraints of the rather unwieldy, predefined, straight-sided 'Hat' shape I was very pleased with the degree of anatomical accuracy. I normally create designs using much more forgiving curves and am able to stretch and distort edges to accommodate. Not so 'The Hat'! It was a real challenge to produce creatures that didn't just look 'boxy' and rigid.

After working out the two designs it was time to start painting. Being something of a dinosaur myself, I still enjoy the process of working with traditional materials rather than digitally, embracing the handmade qualities and slight variations that naturally arise. For both of these paintings I chose to use watercolours.

The first version was more of a challenge in terms of size, colouration and detail, and there were many times when I regretted being so ambitious! I chose to outline this one using pencil in order to help clarify the shapes without resorting to the starkness of inky black lines.

The second version keeps to a much simpler, monochromatic colour scheme so that the individual tiles are more easily recognised. The use of a thin, black fineliner pen seemed appropriate for this one. In each case all of the final outlining was done freehand as I sought to maintain an organic quality of line throughout and avoid a mechanical look ( - and I certainly don't trust myself with a pen and a ruler!)

The colour schemes took a lot of careful consideration. For aesthetic reasons I chose to arrange each coloured tile so that it sits in isolation, avoiding any matching of colours at adjacent edges or corners. I also tried to find a pleasingly balanced arrangement of the four colourways and to minimise the occurrences of nearby tiles of the same orientation having the same colour. This proved to be unexpectedly tricky but I was happy with the end result. Obviously the colours can be changed easily through digital editing and I've already produced a wide range of dramatically different colour schemes using my very rudimentary IT skills and a basic editing app.

I see these designs as being ideal for such things as fabrics, wallpapers, floor tiles, wall tiles, shower curtains, duvet covers, cushions, tea towels, shirts, pyjamas, backpacks, lunchboxes, mugs, greetings cards, pencil cases, book covers... even hats!

I hope you like them!

160 Ildikó Fekete 31 Hungary

As a professional Easter egg painter, I thought it would be a challenge to apply Einsten tiles to the surface of the egg by using traditional tools and techniques.

While the beauty of Einsten tile is its unrepetitiveness in the infinite plane, its beauty on the egg is the infinite repetitiveness. Since belts are very common on traditional Easter eggs, I felt that this solution brought together modern and traditional Easter eggs.