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The Mathematics of Various Entertaining SubjectsResearch in Recreational Math$
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Jennifer Beineke and Jason Rosenhouse

Print publication date: 2015

Print ISBN-13: 9780691164038

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691164038.001.0001

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Minimalist Approaches to Figurative Maze Design

Minimalist Approaches to Figurative Maze Design

Chapter:
(p.29) 3 Minimalist Approaches to Figurative Maze Design
Source:
The Mathematics of Various Entertaining Subjects
Author(s):

Robert Bosch

Tim Chartier

Michael Rowan

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691164038.003.0003

This chapter demonstrates that simple mathematical methods can be used to design mazes that resemble user-supplied target images. The first approach discussed here is the TSP method, which involves converting the target image into a stipple drawing, and then treating the dots as the cities of a Traveling Salesman Problem (TSP). Another approach involves replacing the TSP with a much easier optimization problem—the problem of finding a minimum spanning tree (MST). The chapter then introduces a hybrid approach that produces mazes that have both the random textures of the original TSP Art and MST Art mazes and also the directional textures of the phyllotactic mazes. Finally, the chapter describes how to form a maze by constructing an image mosaic out of the vortex tiles.

Keywords:   mazes, maze design, Traveling Salesman Problem, minimum spanning tree, seeded stippling, phyllotactic mazes, vortex tiles

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