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Everything about Binary tiling
Tiling of the hyperbolic plane
In geometry, a binary tiling is a tiling of the hyperbolic plane, resembling a quadtree over the Poincaré half-plane model of the hyperbolic plane. The tiles are congruent, each adjoining five others. They may be convex pentagons, or non-convex shapes with four sides, alternatingly line segments and horocyclic arcs, meeting at four right angles. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Binary tilingA 5-minute orientation
- Pick up a classic book: Java software solutionsThe most-reprinted book on the subject
- Read the landmark paper: Phason elastic constants of a binary tiling quasicrystalCited 31 times
- Go sideways: TessellationA closely related topic
- Go sideways: Hyperbolic geometryA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
📚 Books worth reading
Java software solutionsLewis, John, John E. Lewis Ph. D. · 1997
Symmetries, Integrable Systems and RepresentationsKenji Iohara · 2012- 📕Expansion of Tiling Algorithm to include non-binary classificationDavid McTavish · 1999
Practical Game Development with Unity and BlenderAlan Thorn · 2014
Combinatorial Image AnalaysisReneta P. Barneva · 2012
Game of life cellular automataAndrew Adamatzky · 2010
ICICS 2017 · 2017
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Tessellation A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In…
- Hyperbolic geometry In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate…
- Horocycle In hyperbolic geometry, a horocycle (from Greek roots meaning "boundary circle"), sometimes called an oricycle or limit circle, is a curve of constant…
- Poincaré disk model In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which all points are inside…
- Circle Limit III Circle Limit III is a woodcut made in 1959 by Dutch artist M. C. Escher, in which "strings of fish shoot up like rockets from infinitely far away" and…
- Order-3 apeirogonal tiling In geometry, the order-3 apeirogonal tiling is a regular tiling of the hyperbolic plane. It is represented by the Schläfli symbol {∞,3}, having three regular…
- Pentagonal tiling In geometry, a pentagonal tiling is a tiling of the plane where each individual piece is in the shape of a pentagon. A regular pentagonal tiling on the…
- Hypercycle (geometry) In hyperbolic geometry, a hypercycle, hypercircle or equidistant curve is a curve whose points have the same orthogonal distance from a given straight…