A tessellation pattern is one composed of shapes without gaps or overlaps. Tessellations can use simple geometric shapes (such as squares and triangles) or much more complex or irregular shapes (such as stylized birds or fish) that have been designed to fit together neatly in a repeating pattern. Here, we introduce this fun type of pattern and guide you through how to make tessellations.

## What Does Tessellation Mean?

The dictionary definition of tessellations is to arrange in a mosaic pattern. However, that’s very narrow, and doesn’t capture the breadth of meaning of tessellations in math, nature, and design.

Tessellation is when you put shapes together to create a pattern without gaps between the shapes. For example, squares can be tessellated, because when you place them next to each other, there are no gaps between them. Circles don’t tessellate, because there will always be gaps between them. However, you can solve this by adding another shape between the circles (such as a curved-sided diamond) to make a tessellating pattern.

### Tessellations in Math

Like many other repeating or geometric designs, tessellations are rooted in mathematics. Math divides tessellations into three main categories: regular, semi-regular, and demi-regular (other).

Regular tessellations in math are shapes like squares, triangles, and hexagons that fit together precisely. You could cover a flat surface with these shapes of the same size and not have any white space between.

A semi-regular tessellation is made of two or more kinds of shapes. Think of octagons within squares in between them, or a 7 sided polygon (heptagon) with star shapes between. Alone, the octagon or 7 sided polygon wouldn’t tessellate, but with the insertion of another shape, they can.

Demi-regular tessellations are those that use non-regular or non-geometric shapes, such as those popularized by M.C. Escher (above).

### Tessellations in Nature

A honeycomb is a perfect example of a tessellated pattern in nature: tiny hexagons repeated without gap or overlap. So are the diamond-shaped scales of snake skin and the knobbled surface of a pineapple.

While you won’t find many other examples of precise, mathematically accurate tessellated patterns in nature, various organic patterns come close and can be used as inspiration for creating tessellated patterns. Think: the unfurling petals of a flower, birds’ feathers, or pinecones.

### History of Tessellations in Design

Tessellations have been used for centuries, and across cultures, in various aspects of design. Think of tiles or mosaics used in Ancient Rome, medieval Persia, or Morocco.

In modern design, no single artist has been as influential as M.C. Escher (1898–1972). The work of the Dutch graphic designer became especially popular in the late 20th century and after. Escher was inspired by math and the tessellated Moorish design and architecture of the Alhambra in Southern Spain. He used mathematical grids as the basis for creating complex interlocking designs. His work shows how creative it’s possible to be with tessellated patterns while following mathematical principles of order and regularity.

## Get Inspired by Tessellation Patterns

Quirky Surface Pattern: Tessellating Patterns.

## How to Tessellate a Shape

If you’d like to learn how to create a tessellation pattern, there are a couple of ways to do so. Shapes can be tessellated freehand on paper or using graphic design computer programs. Tessellating freehand will take much longer, but can be done if you have patience or don’t have access to advanced programs. Otherwise, follow the steps below to learn how to tessellate a square shape with a pattern inside it in Photoshop and Illustrator. Similar principles can be applied to tessellating other shapes.

If you’re not already proficient in using these programs, take an introductory or refresher course before you begin learning how to make tessellations.

### Step 1: Sketch Out a Rough Idea on Paper

Gather inspiration for tessellation pattern ideas from nature, geometry, and other artists. Start by sketching out the central component of your pattern on paper first, until you are happy with how it looks. Whether you’re continuing with hand-drawing or moving onto a computer program later, this step is the same.

### Step 2: Take Your Pattern to Photoshop

After starting Adobe Photoshop, open up a new file and create a grid.

Now, you can either draw your pattern freehand over this grid, or you can click View → Snap to → Grid to draw in straight lines. This is particularly useful if you are drawing a pattern composed of squares. If you use this function, you might want to turn it off at times to free-draw certain parts of your pattern.

Begin your drawing by creating a large square on the grid, and then drawing your pattern within it. Don’t worry if your sketch isn’t perfectly neat, as you’ll be able to clean it up later in Illustrator.

Save your sketch before exiting Photoshop.

### Step 3: Import Your Sketch Into Illustrator

Import your Photoshop sketch into your Illustrator program by clicking on File → Place, and then selecting your sketch from where you saved it.

It’s now time to fine-tune your sketch by perfecting the lines and selecting colors.

These courses on tessellating quirky surface patterns and making super easy tessellating patterns in Illustrator (with tessellation pattern templates) give step-by-step instructions on using computer programs to create your designs and then tessellating them. They require some familiarity with the programs, so are best suited to intermediate graphic designers, or those with more than beginners’ knowledge.

### Step 4: Repeat the Pattern

Once you’ve finalized the central component of your pattern and the lines, colors, and shapes are how you want them to be, it’s time to repeat them to complete the tessellated pattern. This is quite straightforward with geometric shapes.

Start by placing a single square tile in the top left-hand corner, and copying and pasting it below, repeating that step until you have a full row. Then, copy and paste that entire row, and repeat. Make sure that the shapes align perfectly and that there’s no white lines between them.

## Tessellation Patterns

The semi-random color scheme of this pattern makes it look much more complex than it is, as it is a simple pattern of repeating triangles. Triangles are an ideal shape for tessellating patterns, and you can make them more or less complicated by varying the sizes of the triangles and the lengths of their sides.

Tiles and mosaics have been used in various ways for centuries and are usually composed of patterns that repeat and slot together neatly.

Computer programs are essential for creating some complex tessellating patterns, as patterns such as this would be extremely challenging to perfect by drawing freehand.

This complex pattern is inspired by M.C. Escher tessellations, which often used animal subjects.

Tessellating diamonds and semi-circles give the impression of a three-dimensional cube decorated with half-moon shapes.

While this design looks complex, it is fundamentally composed of easy-to-repeat squares with contrasting designs within them.

All kinds of shapes can be used to make tessellating patterns, as long as they’re designed leaving no gaps between them.

## Tessellations, Rotations, Reflections—Oh My!

Patterns and Principles: Learn to Create Patterns by Using Principles.