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Non-local growth of Penrose tilings Ross, Elissa Joanne
Abstract
The problem of mistakes in Penrose tilings will be investigated. Specifically, we will consider the non-locality of any growth process that attempts to avoid errors in the construction of a tiling of the plane by Penrose rhombs. This discussion will be framed by considering the one dimensional version of this problem for Fibonacci Tilings, the aperiodic tilings of the line. These considerations lead to the conclusion that local growth algorithms for correct Penrose tilings of the plane do not exist.
Item Metadata
| Title |
Non-local growth of Penrose tilings
|
| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
2005
|
| Description |
The problem of mistakes in Penrose tilings will be investigated. Specifically,
we will consider the non-locality of any growth process that attempts to avoid
errors in the construction of a tiling of the plane by Penrose rhombs. This
discussion will be framed by considering the one dimensional version of this
problem for Fibonacci Tilings, the aperiodic tilings of the line. These considerations
lead to the conclusion that local growth algorithms for correct Penrose
tilings of the plane do not exist.
|
| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2009-12-15
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
|
| DOI |
10.14288/1.0080073
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2005-11
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| Campus | |
| Scholarly Level |
Graduate
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| Aggregated Source Repository |
DSpace
|
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.