Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [tessellations]

For question on Tessellations, the process of creating a two-dimensional plane using the repetition of a geometric shape with no overlaps and no gaps.

Tessellation is the process of creating a two-dimensional plane using the repetition of a geometric shape with no overlaps and no gaps. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art of M. C. Escher, who was inspired by studying the Moorish use of symmetry in the Alhambra tiles during a visit in 1922. Tessellations are seen throughout art history, from ancient architecture to modern art.

217 questions
3
votes
0 answers

The maths behind 'Sky and Water 1' by Escher

I've been inspired by Eschers 'Sky and Water1' woodcut, his work is so mindblowing, it got me thinking whats the maths behind it. How did he do it?
kelsey
  • 31
3
votes
1 answer

One element space tessellations

Disclaimer: i am bioinformatician and programmer, please excuse if my wording and definitions are far from elegant and occasionally imprecise. Intro: I am interested in space tessellations of n dimensional spaces with following properties: 1 a…
Maciej
  • 153
  • 6
3
votes
1 answer

A Voronoi diagram with two dimensional generators on a "warped" plane

Consider this set of two dimensional generators (red polygons top left). A Voronoi diagram of these polygons is shown at bottom left. Now consider the same set of two dimensional generators on some "warped" surface (e.g. this banded surface at top…
digitalmaps
  • 133
2
votes
1 answer

11 sided irregular shape that tessellates

My friend was fiddling around on the triangle when he created an irregular heptagon with it not able to tessellate. He then asked me if I could create an 11 sided irregular polygon that is able to tessellate by changing a side AB. He told me there…
Stevo
  • 241
1
vote
0 answers

Can "the hat" tessellation be recreated using hexagons marked with "hat" borders and some simple rules?

An aperiodic tiling shape, "the hat" was discovered recently. If you split a tiled planed into hexagons, containing the borders of the hat, would there be a finite number of unique hexagons. If so, would there be a simple rule to use said hexagons…
Megasaur
  • 111
1
vote
1 answer

Round random points to the nearest vertices of a regular tessellated hexagon

For a simulation I need to be able to take points that are scattered around randomly and move their point to the nearest vertex of a tessellated regular hexagon. That way each point is sitting on a vertex of the pattern. Below is a diagram, showing…
J.Doe
  • 485
0
votes
3 answers

Can I fix a tiled floor with only one wrong tile left?

If I have a $n\times m$ rectangular floor completely tessellated with $2\times 2 $ and $1 \times 4$ tiles and it now happens that I accidentally break one of those (no matter which one)- Can I then fix my misfortune if I only have one tile of the…
user161516
0
votes
1 answer

Tesselation beeing used in a game board

I like to know what is the math behind the outlines of these…
user2567875
  • 123
0
votes
0 answers

what is the theoretical solution to Voronoi domain distribution for 2D random point sets

Consider a large set of random points in 2D plane generated by Poisson process. And consider only the finite Voronoi domains generated using these points. Is there a theoretical solution to the Voronois domain distribution if the size of the points…
Wan-Qing Yu
  • 1