Theory of computation | Euclidean tilings | Aperiodic tilings | Undecidable problems

Wang tile

Wang tiles (or Wang dominoes), first proposed by mathematician, logician, and philosopher Hao Wang in 1961, are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them. The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern. (Wikipedia).

Wang tile
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The Story of Chinese Character : 玉

玉 depicts a string of jade pendants. After symbolization, 玉 looks the same as 王, so a dot is added to distinguish 玉 from 王, but when 玉 acts as an radical, the dot is omitted.

From playlist The Story of HanZi (Chinese Characters)

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The BuShou of HanZi :广

A brief description of the BuShou of 广.

From playlist The BuShou of HanZi

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Nathalie Aubrun: About the Domino problem on finitely generated groups - Lecture 1

Abstract: Subshifts of finite type are of high interest from a computational point of view, since they can be described by a finite amount of information - a set of forbidden patterns that defines the subshift - and thus decidability and algorithmic questions can be addressed. Given an SFT

From playlist Mathematical Aspects of Computer Science

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Emmanuel Jeandel : The undecidability of the domino problem

Abstract: One of the most fundamental problem in tiling theory is to decide, given a surface, a set of tiles and a tiling rule, whether there exist a way to tile the surface using the set of tiles and following the rules. As proven by Berger in the 60's, this problem is undecidable in gene

From playlist Combinatorics

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The BuShou of HanZi :田

A brief description of the BuShou of 田.

From playlist The BuShou of HanZi

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SAT Prep: Test 5 Section 7 Part 1

Problems 1-5 starting on page 669

From playlist SAT Preparation

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History of Science and Technology Q&A (December 1, 2021)

Stephen Wolfram hosts a live and unscripted Ask Me Anything about the history of science and technology for all ages. Find the playlist of Q&A's here: https://wolfr.am/youtube-sw-qa Originally livestreamed at: https://twitch.tv/stephen_wolfram 0:00 Start stream 2:02 SW begins talking 2:4

From playlist Stephen Wolfram Ask Me Anything About Science & Technology

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Ancient Chinese Historian Describes The Xiongnu // Before The Mongols // Book of Han (111 AD)

A thousand years before the Mongols, China had to build the world's longest wall to defend against incursions from a truly ancient enemy: The Xiongnu. Here we have an extract from the Book Of Han that describes their customs and origins - a people amongst whom "the strong and robust were h

From playlist Mongols

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The BuShou of HanZi : 金

A brief description of the BuShou of 金.

From playlist The BuShou of HanZi

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The BuShou of HanZi :宀

A brief description of the BuShou of 宀.

From playlist The BuShou of HanZi

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The BuShou of HanZi :禾

A brief description of the BuShou of 禾.

From playlist The BuShou of HanZi

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The BuShou of HanZi :舌

A brief description of the BuShou of 舌.

From playlist The BuShou of HanZi

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The BuShou of HanZi :片

A brief description of the BuShou of 片.

From playlist The BuShou of HanZi

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Jorge Kurchan - Glass transitions 3

PROGRAM: US-India Advanced Studies Institute on Thermalization: From Glasses to Black Holes PROGRAM LINK: http://www.icts.res.in/program/ASIT2013 DATES: Monday 10 Jun, 2013 - Friday 21 Jun, 2013 VENUE: Indian Institute of Science (IISc), Bangalore The study of thermalization has become an

From playlist US-India Advanced Studies Institute on Thermalization: From Glasses to Black Holes

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Boris Solomyak: Lecture on Delone sets and Tilings

Abstract: In this lecture we focus on selected topics around the themes: Delone sets as models for quasicrystals, inflation symmetries and expansion constants, substitution Delone sets and tilings, and associated dynamical systems. Recording during the Jean-Morlet chair research school "T

From playlist Dynamical Systems and Ordinary Differential Equations

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The BuShou of HanZi :石

A brief description of the BuShou of 石.

From playlist The BuShou of HanZi

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Fin Math L7: The Wang transform and the Lorenz curve in Black-Scholes-Merton

Welcome to Financial Mathematics. In this lesson we continue our discussion about the Wang transform and we also introduce an interesting connection with the Lorenz curve, a very useful instrument originally developed in the inequality studies' literature. As we shall see, the use of Wang

From playlist Financial Mathematics

Related pages

DNA | Quasicrystal | Hao Wang (academic) | Tessellation | Penrose tiling | Procedural texture | Cellular automaton | Formal system | Decision problem | Turing machine | Aperiodic tiling | Edge-matching puzzle | Halting problem