This effect originates from the ignorance of interdependences that occur outside the bounded region.
2.
However, any bounded region, no matter how large, will be repeated an infinite number of times within the tiling.
3.
In the upper-left corner we see a shape; that is, a bounded region with a well-behaved boundary.
4.
The Hilbert space formulation of boundary value problems for the Laplacian on a bounded region in the plane proceeds from the following data:
5.
All of the bounded regions surrounded by toothpicks in the pattern, but not themselves crossed by toothpicks, must be squares or rectangles.
6.
If none of these patterns is present at t = 0, then in any bounded region the pattern eventually settles down to all zeros.
7.
The surface of a sphere may be divided by line segments into bounded regions, to form a "'spherical polyhedron " '.
8.
A word structured as a " count " half and a " pointer " half facilitates the use of bounded regions of memory, notably stacks.
9.
If a Poisson point process is defined on some underlying space, then the number of points in a bounded region of this space will be a Poisson random variable.
10.
In this way, Schaeffer's system can be used to apply any function to any bounded region of the state space, showing that this automaton rule is physically universal.
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