Introduction: Tessellating Cats Decoration or Puzzle

I like cats, I like group projects and I like puzzles (as a social activity).
I also like to cut stuff out using my scroll saw - though cutting lots of the same item sucks and would be MUCH easier with a laser cutter (pardon me while I wipe the drool off my chin thinking about an Epilog laser cutter :-).

This instructable describes how I made a set of cat puzzle pieces as a gift for my daughter's teacher.  I made cats that interlocked, in a space filling, repeating pattern, called a tessellation.  Good examples of tessellation can be found in the works of M.C. Escher - 

My daughter and her friends decorated lots of cats, which were then given to her teacher.  We had a bunch of extra cats, which family members decorated and are pictured here.  (Too bad I forgot to take a picture of ALL the cats that were given away - this was several years ago and the teacher has since retired).

Tessellations are wonderful for group projects because each person can decorate the tiles in a unique fashion, but they can also all be combined to make a larger focal piece.  And, since all the pieces interlock, they can be assembled and reassembled in numerous variations.

Cat tessellations can also be hung together for a window/wall decoration, or, with added magnets, be fun fridge or white-board decorations.  It might be fun to make a set of cat pieces for Halloween decorations.

Step 1: Select Base Tile Shape

Tessellations are repeating tile-shapes, and can can be made using several base shapes.  Common shapes used are equilateral triangles, diamond, and squares.  The base shape must fit closely together, with NO spaces in between individual pieces... think floor tiles.

1. I used a square base shape.
2. I modified the square using the technique of TRANSLATION -  removing a part from one side of the base shape, and SLIDING over to the opposite side.  I drew cat ears on the bottom and SLID the ear shapes up to the top of the square = TRANSLATION.
3.  I wanted to have two different kinds of cats, so I drew one set of ears 'upside down' and SLID it down to the bottom of the square.  The second set of ears will become a skinny cat.

Note:  Here is where you have to decide on the goal of the project: 
1- Have recognizeable cats, no matter how they are decorated or
2 - Give the decorators more options in decoration.  You can make a tessellating piece that is very abstract and let participants draw whatever shapes they can fit on their tile.
The teacher for whom this gift was made was very fond of cats, so I wanted each piece to be recognizeable as a cat.
I've done abstract tessellation tiles for

Step 2: Shaping the Sides of the Cat

Once you have the ears in place, select parts from the sides of the square to form part of a cat silhouette (outline).
1. Draw one side of the fat cat head and SLIDE or translate it to the other side of the square, where it will become the leg of the upside-down skinny cat.
2. Draw the side of the fat cat, and SLIDE it over to become the side of the skinny cat head

Step 3: Finish the Cat Shapes

1. Draw the remaining side of the cats - this is in the center of the square.  The upper curve defines the head of the fat cat and the flank of the skinny cat.  The Lower curve defines the flank of the fat cat and the head of the skinny cat.
2. Close of the bottom of the cat front paws.
3.  Cut cat shapes out of desired material. 
I used heavy book board (like really thick cereal boxes) which I stack cut on my scroll saw.  I cut stacks of 5 or 6 and made about 30 of each type of cat.  Thin plywood would also work fine.  If you want to use acrylic sheet, you will need to use a laser cutter - it is very hard to cut plastics on a scroll saw without the plastic melting from the heat of friction as the blade moves up and down.

.pdf file for those who want to print out a larger copy of the pattern

Step 4: Decorate the Cats

Here is the fun part for a group of people.  Collect colroed pencils, markers, paints etc. and decorate away to your heart's content.  Kids LOVE this part. Cats decorated by my nephew, neice and two aunts.

Step 5: Alternate Method for Tesselation

If you are not a drawing sort, but prefer scissors, you can take a cardstock square and literally cut parts off one side and tape them to the other side of the square.  This is how I made the orignal cat pattern. 
I digitally re-drew the all the steps to make it easier to follow the process that I used to create the tessellating cats.

4th Epilog Challenge

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4th Epilog Challenge

Halloween Decorations Challenge

Participated in the
Halloween Decorations Challenge