Artifacts in black and white
or in any coloured light,
patterns knit by maddest hatters
defy the use of words and letters.
Design or game or maths as art ? -
I really don't know where to start
and how to tell you what I see;
it's mystic, mantra-like to me,
it's puzzling, difficult and vexing,
complex, astounding and perplexing.
And still - it could be after all
just your neighbour's bathroom wall.
Introduction
Chapter 1 Basic Notions
Chapter 2 Size-Alternating
Tilings
Alternating tilings with different sizes of one shape.
Chapter 3 Squares of All Sizes - a Tricky Problem and a Tricky Solution
Chapter 4 Shape-Alternating Tilings of the Plane
Chapter 5 Alternating Tilings of
the Plane Using N-gons and M-gons
An introduction to mosaics made from m-sided and n-sided polygons
Chapter 6 The Hall of Fame - A Gallery
of Mosaics
Neat alternating tilings of the plane using n-gons and m-gons.
We try to find those with the smallest number of prototiles.
We give all solutions for pairs (n,m) where n, m < 11.
Chapter 7 The Ones That Did Not Quite
Make It.
Some interesting mosaics with a larger than minimum number of prototiles.
Chapter 8 The Toolbox
General construction methods for neat alternating tilings.
Upper bounds for the minimum number of prototiles for certain (n,m).
Chapter 9 The Existence Theorem of Neat
Alternating Tilings of the Plane
Using N-gons and M-gons.
We find upper bounds for the minimum number of prototiles.
Chapter 10 Symmetric Tiles
Neat alternating tesselations whose tiles are symmetric.
Chapter 11 Neat Alternating Tilings of the Plane
Using N-gons, M-gons and P-gons.
We find solutions for all triples (n,m,p) where n, m, p < 11.
Chapter 12 Neat Alternating Tilings of the Plane
Using N-gons, M-gons, ...., and Q-gons.
We prove a general existence theorem for neat alternating
tilings of the plane of type (n,m,p,...,q).
We find upper bounds for the minimum number of prototiles.
Chapter 13 Nowhere-Neat Tilings of the Plane
We try to find all mosaics with one or two prototiles.
Chapter 14 The Existence Theorem and the Extension
Theorem for Nowhere-Neat Tilings.
We find upper bounds for the minimum number of prototiles.
Chapter 15 Nowhere-Neat Alternating Tilings of the Plane
Literature