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?

  • 5
    Tessellation, by definition, is one shape repeated.
    – Scott
    Jan 21 '20 at 11:43
  • So we could say a tessellation of intricate shape but aren't intricate shapes themselves contains tessellations?...
    – user147753
    Jan 21 '20 at 11:55
  • 1
    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
    – joojaa
    Jan 23 '20 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):

enter image description here

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

enter image description here

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.

There's more info here.

  • My understanding (which could be wrong) is that Tessellation isn't merely the repeating of something. It's the repeat of one shape. If there is more than one shape, the result is a pattern, not a tessellation. Your first image, Escher.. yes Tessellation.. your second image is a repeat of multiple shapes and therefore a pattern, not a tessellation.
    – Scott
    Jan 21 '20 at 23:14
  • 1
    @Scott my understanding is that tessellation is the repeat of one or more shapes; a "tile" can be composed of multiple shapes. Islamic art such as the tiling of Alhambra palace is considered a tessellation. It seems there are multiple types of tessellation patterns.
    – Luciano
    Jan 22 '20 at 0:30
  • 1
    hmm.. maybe. I always thought a tessellation is a pattern, but a pattern is not necessarily a tessellation.
    – Scott
    Jan 22 '20 at 0:36
  • tessellations.org mentions four different meanings of the word. (@Scott)
    – Wolff
    Jan 22 '20 at 19:06
  • .. but.. @Wolff .. all 4 of those allude to a single shape being repeated. Sometimes merely not uniform shapes. There's no mention if multiple shapes being repeated (as in a pattern tile).
    – Scott
    Jan 23 '20 at 1:55

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