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Python Programming in OpenGL 
 
 
A Graphical Approach to Programming 
 
 
 
 
 
 
 
 
 
 
 
 
Stan Blank, Ph.D. 
Wayne City High School 
Wayne City, Illinois 
62895 
 
October 6, 2009 
 
 
Copyright 2009
 2
Table of Contents 
Chapter 1 Introduction......................................................................................6 
Chapter 2 Needs, Expectations, and Justifications ..........................................8 
Section 2.1 What preparation do you need? ...............................................8 
Section 2.2 What hardware and software do you need?.............................8 
Section 2.3 My Expectations .......................................................................9 
Section 2.4 Your Expectations ....................................................................9 
Section 2.5 Justifications...........................................................................10 
Section 2.6 Python Installation ..................................................................11 
Exercises .....................................................................................................12 
Chapter 3 Your First Python Program ............................................................13 
Section 3.1 Super-3 Numbers ...................................................................13 
Section 3.2 Conclusion .............................................................................21 
Exercises .....................................................................................................21 
Chapter 4 Your First OpenGL Program..........................................................23 
Section 4.1 The Interactive Python Interpreter ..........................................23 
Section 4.2 Introducing Python OpenGL...................................................24 
Section 4.3 Odds, Ends, and Terminology ................................................29 
Section 4.4 Conclusion .............................................................................31 
Exercises .....................................................................................................31 
Chapter 5 2 Dimensional Graphics ................................................................33 
Section 5.1 Plotting Points ........................................................................33 
Exercises .....................................................................................................37 
Section 5.2 Plotting 2D Functions .............................................................41 
Exercises .....................................................................................................44 
Sections 5.3 Parametric Equations .............................................................50 
Exercises .....................................................................................................53 
Section 5.4 An Example from Physics ......................................................65 
Exercises .....................................................................................................74 
Section 5.5 Polar Coordinates...................................................................80 
Section 5.6 Conclusion .............................................................................89 
Exercises .....................................................................................................90 
Figures for Exercises 2-15...........................................................................95 
Chapter 6 Patterns and Chaos in 2 Dimensions ............................................99 
Section 6.1 PySkel ....................................................................................99 
Section 6.2 Some Interesting Patterns....................................................101 
Exercises ...................................................................................................106 
Figures for exercises 7, 8, 9, and 10..........................................................111 
Section 6.3 The Chaos Game.................................................................112 
Exercises ...................................................................................................124 
Section 6.4 The Barnsley Fern...............................................................129 
Exercises ...................................................................................................133 
Section 6.5 Chaos and the Logistic Map................................................136 
Exercises ...................................................................................................143 
Section 6.6 Predator-prey Relationships.................................................148 
Exercises ...................................................................................................152 
 3
Chapter 7 Strange Attractors and Beautiful Fractals ....................................154 
Section 7.1 Lorenz and the Weather.......................................................154 
Exercises ...................................................................................................162 
Section 7.2 Phase Portraits and Paint Swirls ..........................................167 
Exercises ...................................................................................................170 
Section 7.3 Mira (Look?) .........................................................................172 
Exercises ...................................................................................................174 
Section 7.4 The 3-Body Problem ............................................................175 
Exercises ...................................................................................................178 
Section 7.5 Newton’s Method and the Complex Plane ...........................183 
Exercises ...................................................................................................193 
Addendum: ................................................................................................203 
Addendum II: .............................................................................................203 
Section 7.6 The Julia Set .......................................................................205 
Exercises ...................................................................................................211 
Section 7.7 Explorations with the Mandelbrot Set ...................................222 
Exercises ...................................................................................................240 
Chapter 8 2D Animation...............................................................................246 
Section 8.1 Follow the Bouncing Ball ......................................................246 
Exercises ...................................................................................................255 
Section 8.2 A Little Gravity! .....................................................................261 
Exercises ...................................................................................................264 
Section 8.3 A Little MORE Gravity... a 2-Body Simulation ......................265 
Exercises ...................................................................................................279 
Section 8.4 The REAL 3 Body Problem ..................................................281 
Exercises ...................................................................................................291 
Section 8.5 From 3Body to NBody Using Arrays.....................................294 
Exercises ...................................................................................................307 
Section 8.6 Navigating the Stars ............................................................309

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