# What is the difference between an intricate shape (common in ornate art) and tessellation?

I assume that the difference between an intricate shape and a tessellation is as follows:

A tessellation is always repetitive in group-units while an intricate shape is repetitive sub-group-units, thus could be defined as a tessellation (or as including tessellation) by itself as well as can be used to make tessellations.
repetitive == two or more;

What is the difference between an intricate shape (common in ornate art) and tessellation?

• Tessellation, by definition, is one shape repeated. Jan 21, 2020 at 11:43
• So we could say a tessellation of `intricate shape` but aren't intricate shapes themselves contains tessellations?...
– user147753
Jan 21, 2020 at 11:55
• The word tesselation like all words does not have a fixed meaning like any natural language word. There are entire industries that use the word tesselation to just mean split up to smaller parts (3D graphics), repeat steps (engineering) ... while others define it as using same tile etc Jan 23, 2020 at 6:57

(I'm no mathematician so bear with me. Tessellations are a complex subject so I'll try to keep it short.)

A tessellation is a repetition of a "tile" (one or more geometric shapes with no gaps or overlaps) in a plane to form a pattern. There are several types of tessellation patterns. For example a honeycomb is a regular tessellation (all sides and angles are equivalent):

The mosaics in the Alhambra palace are non-regular tessellations (there are no restrictions regarding the shapes used or their arrangement around vertices):

Intricate shapes have many elements arranged in a complex manner; in this context it just means that it has complex details. It's a single image with complex shapes. It will only be a tessellation if

So your tessellation can be composed of tiles with intricate shapes.

Look at the example below. It's both composed of intricate shapes (each bird tile) and it's a tessellation semi-regular (there are two distinct bird tile shapes). Bonus: the bricks on the wall can also be considered another tessellation pattern:

Wikipedia also tells us:

A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one shape and with every corner identically arranged.
... A tiling that lacks a repeating pattern is called "non-periodic". An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern.