# Harriet Fell's Mathematical Images

© Harriet Fell 2012
#### From Math for Tanabata

This image and others are part of the Art Exhibit at the 2013 Joint Mathematics Meetings.

You can make your own images like this using Math4Tanabata.

© Harriet Fell 1994
#### Coloring of the Unit Disk ala Dubuc and Malik

Dubuc and Malik (Convex hull of powers of complex number, trinomial equations and the Farey sequences, Num. Algorithms, 2 #1, pp. 1-32) note that the convex hull of the powers 1, z, z^{2}, z^{3}, . . . of a complex number z, in the interior of the unit disk, is a polygon. They define the *color* of the number to be the number of vertices of this polygon.

© Harriet Fell 1994
#### Coloring 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 - (z^{n} - 1).im / (z^{n} - 1).re| < epsilon. That is, the slope of the line through z and 1 differs from the slope of the line through z^{n} and 1 by less than epsilon. For this image, epsilon = 0.02 and the highest power of z considered is 24.

Click here for related colorings.

Harriet J. Fell

College of Computer Science

Northeastern University, Boston, MA 02115

Phone: (617) 373-2198

Email:

The URL for this document is: http://www.ccs.neu.edu/home/fell/mathGraphics.html

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