I would appreciate if you could send me, by e-mail: jswlamb@imperial.ac.uk, as soon as you have it ready, but no later than by the end of this week, a short description of your project, consisting of a brief description of what you plan to do or cover, and which sources you intend to use (at present). I will then review and provide some commentary where usful. Thank you!
Sunday 31 May 2015
Wednesday 27 May 2015
Recommended literature
(For most of the references, I provide a link to an electronic copy in djvu or pdf. I would be interested if any of you have additional recommendations of interesting articles or useful references.)
B. Grünbaum, G. Shephard. Tilings and Patterns. 1987
The only attempt ever to provide a comprehensive theory of tilings and patterns. e-link
M. Senechal. Quasicrystals and Geometry. 1996
A very gentle and readable introduction into aperiodic order with historical context. The mathematics is less well developed in this book, but it is a recommended introductory read. e-link
M. Klemm. Symmetrien von Ornamenten und Kristallen. 1982
This book contains a detailed exposition of the work of Bieberback and Frobenius. As far as I know it is only available in German. I would be interested if anyone found this material also in an English text. e-link
C.E. Horne. Geometric Symmetry in Patterns and Tilings. 2000
Text on symmetry with a design flavour. e-link
M. Baake and U. Grimm. Aperiodic order. 2013
A comprehensive mathematical introduction to aperiodic order. e-link
H. Hiller. The Crystallogrphic restriction in Higher Dimensions. Acta Cryst. (1985). A41, 541-544
A short paper detailing the argument on how to compute the lowest dimension in which you can find a rotation of a given order in a crystallographic group. e-link
N.G. de Bruijn. Algebraic theory of Penrose's non periodic tilings of the plane. I, II. Federal. Aka. Wetensch. Indag. Math. 43 (1981), 39-66.
Papers in which the projection property of the Penrose tilings was first revealed. e-link
C. Goodman-Strauss. Can't decide? Undecide! Notices of the AMS 57 (2010), 343-356.
Accessible introduction into decidability with mention of tiling problems. The author is a world-expert on tiling theory and the talks on his personal webpages are recommended. e-link
E. Harriss. Socolar and Taylor's aperiodic tile. http://maxwelldemon.com/2010/04/01/socolar_taylor_aperiodic_tile/
Excellent introduction into this topic.
H.J. Woods. The geometrical basis of patter design. Part IV: Counterchange Symmetry in Plane Patterns, Journal of the Textile Institute Transactions 27 (1936):12, T305-T320, DOI: 10.1080/19447023608661695
Probably the first comprehensive treatment of dichromatic colour patterns. e-link
A.L. Loeb. Color and Symmetry. 1978.
My recommendation as an introduction on colour symmetry. But I have no electronic or hard copy and it does not appear to be available in Imperial's library.
T.W. Wieting. Mathematical Theory of Chromatic Plane Ornaments. 1982
Comprehensive but elementary introduction to colour and symmetry. e-link
M. Field, M. Golubitsky. Symmetry in Chaos_ A Search for Pattern in Mathematics, Art, and Nature. 2009
An interesting twist on the theme: periodic patterns generated from the simulation of chaotic dynamical systems. Prof Field is currently at Imperial College and I would think you can do a project in this direction (assisted by him). Check out the beautiful pictures in this book! e-link
Delone, B. N.; Dolbilin, N. P.; Štogrin, M. I.; Galiulin, R. V. A local test for the regularity of a system of points. (Russian) Dokl. Akad. Nauk SSSR 227 (1976), no. 1, 19–21.
Paper where Delone's theorem on local regularity implies global regularity is proved. e-link
B. Grünbaum, G. Shephard. Tilings and Patterns. 1987
The only attempt ever to provide a comprehensive theory of tilings and patterns. e-link
M. Senechal. Quasicrystals and Geometry. 1996
A very gentle and readable introduction into aperiodic order with historical context. The mathematics is less well developed in this book, but it is a recommended introductory read. e-link
M. Klemm. Symmetrien von Ornamenten und Kristallen. 1982
This book contains a detailed exposition of the work of Bieberback and Frobenius. As far as I know it is only available in German. I would be interested if anyone found this material also in an English text. e-link
C.E. Horne. Geometric Symmetry in Patterns and Tilings. 2000
Text on symmetry with a design flavour. e-link
M. Baake and U. Grimm. Aperiodic order. 2013
A comprehensive mathematical introduction to aperiodic order. e-link
H. Hiller. The Crystallogrphic restriction in Higher Dimensions. Acta Cryst. (1985). A41, 541-544
A short paper detailing the argument on how to compute the lowest dimension in which you can find a rotation of a given order in a crystallographic group. e-link
N.G. de Bruijn. Algebraic theory of Penrose's non periodic tilings of the plane. I, II. Federal. Aka. Wetensch. Indag. Math. 43 (1981), 39-66.
Papers in which the projection property of the Penrose tilings was first revealed. e-link
C. Goodman-Strauss. Can't decide? Undecide! Notices of the AMS 57 (2010), 343-356.
Accessible introduction into decidability with mention of tiling problems. The author is a world-expert on tiling theory and the talks on his personal webpages are recommended. e-link
E. Harriss. Socolar and Taylor's aperiodic tile. http://maxwelldemon.com/2010/04/01/socolar_taylor_aperiodic_tile/
Excellent introduction into this topic.
H.J. Woods. The geometrical basis of patter design. Part IV: Counterchange Symmetry in Plane Patterns, Journal of the Textile Institute Transactions 27 (1936):12, T305-T320, DOI: 10.1080/19447023608661695
Probably the first comprehensive treatment of dichromatic colour patterns. e-link
A.L. Loeb. Color and Symmetry. 1978.
My recommendation as an introduction on colour symmetry. But I have no electronic or hard copy and it does not appear to be available in Imperial's library.
T.W. Wieting. Mathematical Theory of Chromatic Plane Ornaments. 1982
Comprehensive but elementary introduction to colour and symmetry. e-link
M. Field, M. Golubitsky. Symmetry in Chaos_ A Search for Pattern in Mathematics, Art, and Nature. 2009
An interesting twist on the theme: periodic patterns generated from the simulation of chaotic dynamical systems. Prof Field is currently at Imperial College and I would think you can do a project in this direction (assisted by him). Check out the beautiful pictures in this book! e-link
Delone, B. N.; Dolbilin, N. P.; Štogrin, M. I.; Galiulin, R. V. A local test for the regularity of a system of points. (Russian) Dokl. Akad. Nauk SSSR 227 (1976), no. 1, 19–21.
Paper where Delone's theorem on local regularity implies global regularity is proved. e-link
Presentation online
As a prelude to your projects, I gave a broad talk on tilings and patterns on wednesday 27 May 11:30-13:00. You find the slides in pdf format in the right hand side margin. Please note that I did not discuss the slides on pages 37-67. I chose to leave these slides in as they may contain starting points for people on projects regarding aperiodic tilings. Possible directions for projects can be found on the final two pages 68 and 69. These suggestions should by no means limit your ambition and I am willing to consider alternative proposals for your project as well. I think that it is essential, though, that you run your projects and plans by my for approval in principle (I will provide concrete deadlines later), so that I can make sure you are on track to be able to finish your project in time.
In a few moments I will post more information about literature resources.
In a few moments I will post more information about literature resources.
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