More Colorings of the Unit Disk Based on an Almost Colinear Condition

Given epsilon > 0, define the color of the complex number z to be the smallest positive integer n such that |(z - 1).im / (z - 1).re - (zn - 1).im / (zn - 1).re| < epsilon. That is, the slope of the line through z and 1 differs from the slope of the line through zn and 1 by less than epsilon.
Photograph of a coloring of the unit disk© Harriet Fell 1994

epsilon = 0.01
maximum power of z = 10

Photograph of a coloring of the unit disk© Harriet Fell 1994

epsilon = 0.1
maximum power of z = 16

Photograph of a coloring of the unit disk© Harriet Fell 1994

epsilon = 0.01
maximum power of z = 16

Photograph of a coloring of the unit disk© Harriet Fell 1994

epsilon = 0.001
maximum power of z = 16

Photograph of a coloring of the unit disk© Harriet Fell 1994

epsilon = 0.3
maximum power of z = 32

Photograph of a coloring of the unit disk© Harriet Fell 1994

epsilon = 0.1
maximum power of z = 32

Photograph of a coloring of the unit disk© Harriet Fell 1994

epsilon = 0.01
maximum power of z = 32

Harriet J. Fell
College of Computer Science
Northeastern University, Boston, MA 02115
Phone: (617) 373-2198
fell@ccs.neu.edu

This page last updated: March 21, 1997 at 1:34 pm.
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