If you need an accessible version of this item please contact JSTOR User Support

Matching Rules and Substitution Tilings

Chaim Goodman-Strauss
Annals of Mathematics
Second Series, Vol. 147, No. 1 (Jan., 1998), pp. 181-223
Published by: Annals of Mathematics
DOI: 10.2307/120988
Stable URL: http://www.jstor.org/stable/120988
Page Count: 43
  • Download PDF
  • Cite this Item

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support
Matching Rules and Substitution Tilings
Preview not available

Abstract

A substitution tiling is a certain globally defined hierarchical structure in a geometric space; we show that for any substitution tiling in Ed, d > 1, subject to relatively mild conditions, one can construct local rules that force the desired global structure to emerge. As an immediate corollary, infinite collections of forced aperiodic tilings are constructed. The theorem covers all known examples of hierarchical aperiodic tilings.

Page Thumbnails

  • Thumbnail: Page 
[181]
    [181]
  • Thumbnail: Page 
182
    182
  • Thumbnail: Page 
183
    183
  • Thumbnail: Page 
184
    184
  • Thumbnail: Page 
185
    185
  • Thumbnail: Page 
186
    186
  • Thumbnail: Page 
187
    187
  • Thumbnail: Page 
188
    188
  • Thumbnail: Page 
189
    189
  • Thumbnail: Page 
190
    190
  • Thumbnail: Page 
191
    191
  • Thumbnail: Page 
192
    192
  • Thumbnail: Page 
193
    193
  • Thumbnail: Page 
194
    194
  • Thumbnail: Page 
195
    195
  • Thumbnail: Page 
196
    196
  • Thumbnail: Page 
197
    197
  • Thumbnail: Page 
198
    198
  • Thumbnail: Page 
199
    199
  • Thumbnail: Page 
200
    200
  • Thumbnail: Page 
201
    201
  • Thumbnail: Page 
202
    202
  • Thumbnail: Page 
203
    203
  • Thumbnail: Page 
204
    204
  • Thumbnail: Page 
205
    205
  • Thumbnail: Page 
206
    206
  • Thumbnail: Page 
207
    207
  • Thumbnail: Page 
208
    208
  • Thumbnail: Page 
209
    209
  • Thumbnail: Page 
210
    210
  • Thumbnail: Page 
211
    211
  • Thumbnail: Page 
212
    212
  • Thumbnail: Page 
213
    213
  • Thumbnail: Page 
214
    214
  • Thumbnail: Page 
215
    215
  • Thumbnail: Page 
216
    216
  • Thumbnail: Page 
217
    217
  • Thumbnail: Page 
218
    218
  • Thumbnail: Page 
219
    219
  • Thumbnail: Page 
220
    220
  • Thumbnail: Page 
221
    221
  • Thumbnail: Page 
222
    222
  • Thumbnail: Page 
223
    223