UMASS Online
92.419 Intro to Mathematica
Kenneth M. Levasseur
Department of Mathematical Sciences
University of Massachusetts Lowell
Lowell, MA 01854
 rug

"Persian" Recursion

Subject

Mathematics, Art

Topic

From the first paragraph of [1]: In this note we present a very simple procedure that produces a variety of attractive patterns resembling Persian rugs. . . . The idea behind the "Persian" recursion is to start with a large square, subdivide into four equal squares, and continue the process until we cannot go any further. An example appears at the top of this page.

Reference(s)

  1. Anne M. Burns, ""Persian" Recursion," Mathematics Magazine, 70(1997) 196-199.
  2. A. K. Dewdney, The Armchair Universe, W. H. Freeman and Co., New York, NY, 1988.
  3. Tommaso Toffoli and Norman Margolus, Cellular Automata Machines: A New Environment for Modeling, The MIT Press, Cambridge, MA, 1987.

Project Idea(s)

  1. Reproduce the patterns in [1] and explore other variations. A BASIC program to do "Persian" recursion is provided in [1]. It would be interesting to compare the efficiency of a Mathematica version of this program with other Mathematica programs that might be constructed.
  2. Other related project ideas are suggested in [1-3]

Prerequisite Mathematics

Modular arithmetic, recursion

Required Programming Level

Recursion

Key Words

Graphics, recursion, art, Persian rugs

Reviewer

K. M. Levasseur (Kenneth_Levasseur@uml.edu)

Archive


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