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The triakis truncated tetrahedron is a convex space-filling polyhedron which is the shape of the Voronoi cell of carbon atoms in diamond. It can be constructed from the ...

WireWorld is a two-dimensional four-color cellular automaton introduced by Brian Silverman in 1987. The rule for the automaton uses the cell's old value a together with the ...

A diamond-shaped neighborhood that can be used to define a set of cells surrounding a given cell (x_0,y_0) that may affect the evolution of a two-dimensional cellular ...

Vince and Bóna (2012) define an assembly tree T for a connected simple graph G on n nodes as a binary rooted tree with n leavesTree Leaf and n-1 internal nodes and satisfying ...

A nexus number is a figurate number built up of the nexus of cells less than n steps away from a given cell. The nth d-dimensional nexus number is given by N_d(n) = ...

The Sierpiński carpet is the fractal illustrated above which may be constructed analogously to the Sierpiński sieve, but using squares instead of triangles. It can be ...

A fractal which can be constructed using string rewriting beginning with a cell [1] and iterating the rules {0->[0 1 0; 1 1 1; 0 1 0],1->[1 1 1; 1 1 1; 1 1 1]}. (1) The size ...

The equation of motion for a membrane shaped as a right isosceles triangle of length c on a side and with the sides oriented along the positive x and y axes is given by where ...

To find the motion of a rectangular membrane with sides of length L_x and L_y (in the absence of gravity), use the two-dimensional wave equation ...

There are three types of cubic lattices corresponding to three types of cubic close packing, as summarized in the following table. Now that the Kepler conjecture has been ...