# Bridges 2010 Regular Paper

Creating and Modifying Images Using Newton's Method for Solving Equations

Stanley Spencer

(Proceedings pages 183–190)

## Abstract

The pictures associated with Newton's Method of finding the roots
of an equation are familiar to mathematicians and non-mathematicians.
The main purpose of this paper is to look at ways by which a
recognisable image can be produced or modified using the same
mathematical process. This paper looks at several ways that an
arbitrary pixel image can be iteratively transformed using Newton
type algorithms. The standard approach of letting the pixels evolve
towards attractors was interesting, but a second approach, one that
inverted the process so that attractors became expellers, looks
fruitful for creating interesting images. The process was designed
to allow equations with up to a hundred roots which created challenges
but also opportunities for meaningful outcomes.

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