Tessellations and Color
When discussing a tiling that is displayed in colors, to avoid ambiguity one needs to specify whether the colors are part of the tiling or just part of its illustration. See also symmetry.
The four color theorem states that for every tessellation of a normal Euclidean plane, with a set of four available colors, each tile can be colored in one color such that no tiles of equal color meet at a curve of positive length. Note that the coloring guaranteed by the four-color theorem will not in general respect the symmetries of the tessellation. To produce a coloring which does, as many as seven colors may be needed, as in the picture at right.
Read more about this topic: Tessellation
Famous quotes containing the word color:
“The great God endows His children variously. To some he gives intellect—and they move the earth. To some he allots heart—and the beating pulse of humanity is theirs. But to some He gives only a soul, without intelligence—and these, who never grow up, but remain always His children, are God’s fools, kindly, elemental, simple, as if from His palette the Artist of all had taken one color instead of many.”
—Mary Roberts Rinehart (1876–1958)