Tessellation Art: Explore and Create Patterns

Tessellation Art Studio

Tessellation is a common decorative motif found in both utilitarian and decorative work, including tiles, mosaics, and floors. It simply means to cover a surface with repeating shapes, without overlap or gaps. M.C. Escher, a Dutch artist, explored tessellation and other mathematical concepts in his artwork.

M.C Escher drew inspiration from Islamic mosaic work that he first saw on a 1936 visit to Alhambra in Granada, Spain. He decided to work with figures instead of tiles and also to incorporate the idea of transformations (figures changing from one to another), most famously in his Metamorphosis print series.

While regular tessellation designs involve only simple triangles, squares, and hexagons arranged in patterns, Escher went far beyond, building complex shapes in the form of animals, insects, and people. He used tools like translation, rotation, reflection, and glide reflection to create his patterns.

Interestingly, a mathematician named Evgraf Fedorov proved in 1891 that there are 17 ways to arrange tiles using translation, rotation, reflection and glide. These four operations are the only ways to move a shape across a flat surface without stretching or changing it, and only 1, 2, 3, 4 and 6-fold rotational symmetries are compatible with filling a plane, which is how Fedorov could prove the number and why it is finite. He of course proved this with math and was working with crystal structures, the same math describes why crystal structures, and snowflakes, show six-fold symmetry, while Escher was able to reproduce all 17 ways artistically.

Escher passed away before fractal work moved into the main stream, but his Circle Limit series looks like tessellation that repeats forever. The tiles shrink infinitely toward the edge, creating self-similarity across scales, which is the defining property of fractals.

Below the tool you’ll find a visual catalog of all 17 wallpaper groups — hover over any pattern to see the hidden symmetry elements at work. It is available in interactive form in the post.

Tessellation Studio

Draw one tile and watch it become repeat.

Tessellation Studio is a pattern-repeating tool. You sketch directly onto the tile on the left, and your drawing instantly repeats across the preview on the right in any pattern you choose, mirror, pinwheel, hex grid, brick, spin, and more.

How to Use It

Start by picking a pattern mode from the toolbar; Mirror XY is a good first choice because it creates instant symmetry from even simple marks. Then draw on the white tile canvas. If you want a square of a premade image, drop you picture into the square photo cutting tool and just as you desire, save and then import into tile.

Use the brush size slider to go from fine lines to bold strokes, and pick your color from the swatches or the color wheel.

For tessellation-style interlocking shapes, try drawing near to just one corner of the tile rather than filling the whole square. The negative space in the pattern becomes the positive space in the adjacent tile. Escher snipped away at his design to get to the final tessellation.

Use In-Tile Symmetry to have your strokes mirror or rotate inside the tile as you draw. Turn on BG Color Cycle to tint alternating tiles different colors. Use Random if you want squiggles of color on the tile.

Scroll to zoom the preview and drag to pan around it. Hit Animate to set the pattern drifting slowly.

When you are happy with your design, click Save Preview to download the full pattern as a PNG.

Square Image Prep

If you want to use a photo as your tile base, use the Square Image Prep tool above to crop and fit it first. Upload your image, drag to position it, use the zoom and rotate sliders to get it just right, then save the square PNG and upload it into Tessellation Studio using the Image button on the tile panel. Draw on top of your photo and tessellate.