How animals get their stripes

From NW-DCSD

Contents 1 Overview 2 Relationship to NWDCSD Goals 3 Developer 4 Subscribed Users 5 Potential Users 6 Assessment 6.1 Survey Links 6.2 Learning Objectives 6.3 Learning Outcomes 7 Dependencies / Prerequisites 8 Module Versions and Dependencies 9 Status 10 Description 10.1 Module Length 10.2 Resources 11 Community Comments

Overview

J. D. Murray (1981) proposed a mathematical model for the biological process

that produces animal coat patterns. The model consists of a system of nonlinear

partial differential equations. Approximating these equations by a finite

difference method requires the solution of large systems of algebraic equations

by the common technique known as Gaussian elimination. However, these systems

are highly susceptible to large round-off error without the technique of

Gaussian elimination with partial pivoting. This module is to give students

in mathematics and computer science an interdisciplinary project from biology

for which the chosen computational algorithm must handle round off error.

The final program executes for ten to fifteen minutes while steady state

is being reached before the user knows whether spots or stripes have formed.

They must make many experimental runs – some which do not yield a coat pattern

and some which do. Thus, students have experience with a sufficiently complex

computational algorithm.

Relationship to NWDCSD Goals

The module involves an interdisciplinary project (biology, mathematics,

computer science) that brings computational thinking to non-computer

science students as well as computer science students.

Developer

Kathie Yerion, Gonzaga University

Subscribed Users

Kathie Yerion, Gonzaga University

Potential Users

Teachers of mathematics courses like numerical analysis, differential

equations, linear algebra, and mathematical biology.

Teachers of computer science courses like algorithms.

Assessment

Survey Links

Instructor and Student Survey Links

Learning Objectives

• The students will learn the techniques of approximating differential equations

by finite differences and approximating the resulting algebraic systems.

• They will compare the techniques of “Gaussian elimination” and

“Gaussian elimination with partial pivoting.”

• They will observe that “Gaussian elimination” causes sufficient round-off error

to ruin approximations, even in this day of powerful computers.

• They will experience a computational method that takes some time to complete,

even in this day of fast computers.

• They will do experimental runs and analysis of the results, seeing experimental

mathematics and computer science.

Learning Outcomes

Through the assignments in the module, we want the students to be able

• to approximate derivatives by finite differences
• to perform the techniques of Gaussian elimination and

Gaussian elimination with partial pivoting on small systems

• to use programs that implement these two techniques of Gaussian elimination
• to understand the systems that result from the finite difference method

for the nonlinear partial differential equations

• to understand the computational method
• to use the program that implements the computational method for the

formation of animal stripes and spots

• to experience that there are inputs for the program that do not yield

“good” results and ones that do.

Dependencies / Prerequisites

Module Versions and Dependencies

Status

Description

Module Length

2 weeks (Shortened version 1 week)

Resources

A finite difference method for modeling the formation of animal coat patterns paper

Assignments For this Module

media:Outline of Assignments for Module on Animal.doc

Community Comments

If you reviewed this module but decided to not try and use it, we would appreciate feedback as to why. Please send an email to Dr. Kathie Yerion (yerion@gonzaga.edu) with any feedback and/or questions.