Patterns Available For Mathematical Wood Sculptures

Patterns are shown here in light and dark. This is a virtual representation of wood types. For instance, light could be realized by maple and dark by walnut. The pattern is given by a set of three numbers:

• element 1: A uniform color within each layer is specified by 0; otherwise 1 specifies that color alternates between quadrants, for instance [brown, white, brown, white].
• element 2: The color remains the same from layer to layer if 0; otherwise 1 specifies that the color alternates from one layer to next. This applies regardless of whether element 1 is a 0 or 1.
• element 3: The top and bottom halves of any quadrant of the figure are symmetric in their color pattern if 0; otherwise 1 specifies that, for each quadrant, the bottom half is antisymmetric relative to the top half.

There are 8 possible permutations of the color pattern. {0,0,0} gives a completely uniform coloring, and the color is arbitrarily assigned as one or the other of the two colors. {1,1,1} gives the optimum non-uniform pattern.