Is there an aperiodic tiling such that approximates space?
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Many aperiodic tilings still have some preferred directions. Think of penrose tilings. Imagine turning a tiling into a network and finding geodesic paths through the network. Are any tilings in 2 3 or 4d random enough so that approximates continuous space on the large scale or do all tilings have preferred directions where paths are shorter?
geodesic tiling network
asked Nov 23 at 20:31
zooby
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Many aperiodic tilings still have some preferred directions. Think of penrose tilings. Imagine turning a tiling into a network and finding geodesic paths through the network. Are any tilings in 2 3 or 4d random enough so that approximates continuous space on the large scale or do all tilings have preferred directions where paths are shorter?
geodesic tiling network
asked Nov 23 at 20:31
zooby
956616
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Many aperiodic tilings still have some preferred directions. Think of penrose tilings. Imagine turning a tiling into a network and finding geodesic paths through the network. Are any tilings in 2 3 or 4d random enough so that approximates continuous space on the large scale or do all tilings have preferred directions where paths are shorter?
geodesic tiling network
asked Nov 23 at 20:31
zooby
956616
Many aperiodic tilings still have some preferred directions. Think of penrose tilings. Imagine turning a tiling into a network and finding geodesic paths through the network. Are any tilings in 2 3 or 4d random enough so that approximates continuous space on the large scale or do all tilings have preferred directions where paths are shorter?
geodesic tiling network
geodesic tiling network
asked Nov 23 at 20:31
zooby
956616
asked Nov 23 at 20:31
zooby
956616
asked Nov 23 at 20:31
zooby
956616
asked Nov 23 at 20:31
zooby
956616
asked Nov 23 at 20:31
zooby
956616
956616
add a comment |
add a comment |
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