Mathematics, Art, and Computing

Paul Fishwick, University of Florida

General Math/Art Links
Open Source Software for Exploration
- 2D Paint and Vector: Gimp Sodipodi
- 2D Animation + Intro to 3D: Processing
- 3D Animation: Blender
- JavaView: Interactive 3D Geometry and Visualization
Numbers and Number Systems:
- History
- basic types: integers, floating point, binary and hexadecimal
- some famous numbers: Pi, e, phi, i
- Case Study: Modular Art 1 2
- Fibonacci sequence and Golden Ratio
  - Rabbit population
  - Fibonacci and the Golden Ratio
  - Case Study: Golden Ratio in Art 1 2 3
- Complex numbers: 1 2
Spaces and SpaceTime
- Coordinate Systems and Views
  - Drawing Systems: Front, Side, Top (Plan) Views, and Orthogonal
  - Cartesian, Polar, Oblique
  - Cylindrical and Spherical
  - Anamorphic Projection
  - Color Spaces: Spaces Causes Color, Vision & Art Pigments
  - Musical Spaces (tracks,composition)
- Perspective
  - Perspective Drawing: 1 2
  - Case Study: Albrecht Durer
  - Multi-Projection Rendering
- Dimensions
- Non-Euclidean Geometry:
  - Compass and Straight Edge
  - Klein View of Geometry
  - Hyperbolic Non-Euclidean World
  - Using Cabri
  - Non-Euclid
  - Information Visualization
  - Case Study: M. C. Escher
Sets
- Ordered (tuples) and unordered
- Layers, objects, grouping and ungrouping in Gimp and Sodipodi
Functions
- Curves: 1 2 3
- Surfaces: 1
- Case Study: Helaman Ferguson
- Transformations 1
- Fractals (recursive functions)
  - General Repository
  - Fractal Music
- Mandelbrot Set (a complex recursive function)
- Case Study: Fractal Artists Ring
- Functional composition (networks of functions)
  - Graphics: Houdini operator network
  - Sound: MAX/MSP
Relations
- drawing 2D graphs with spring-like relations
Reasoning
- Propositional and Predicate Logic
  - Tarski's World
- Logic Diagrams
- Proofs
  - Induction
  - Assortment
  - Geometric Proofs: Introduction Pythagoras
Basic Structures
- Lists, vectors, arrays, stacks, queues, objects
Trees
- Constructive Solid Geometry boolean trees
- BSP Trees
- U. of Maryland Spatial Data Structures
- Case Study: Piet Mondrian
  - Manual Creator
  - Generator
Graphs
- Scene Graphs: van Dam Tutorial
- Wayfinding graphs in architecture and virtual worlds
Topology
Algebraic Structures and Symmetry
- An Introduction to Groups
- Polyhedra: Virtual Polyhedra (George Hart)
- Tiling and Tesselations
  - Tiling
  - Symmetry and Tesselations
  - Aperiodic Tiling: 1 2
  - Hyperbolic Tesselations
  - Hyperbolic Planar Tesselations
Automata and Machines
- Mechanical
- Cellular Automata (CA): 1D CA 1 2 3 4 3D: 1 2 Music: Paper (Todd,Miranda)
- Production/Rule Systems
  - Lindenmeyer (L) Systems: Intro 1 2 LParser
  - Shape Grammars: Shaper2D 3D Shaper
- Finite State Automata: 1
- Markov models
- Turing machines
Advanced Topics
- Dynamical Systems: Wright
- Exploratory Math + Computing Notation: Aesthetic Computing
- Noise (Ken Perlin)
- Line Integral Convolution
- Pattern Matching, Interpolation and Extrapolation
  - Neural Networks for Art
- Optimization with Genetic Art and Music
  - Karl Sims
  - Ken Musgrave and Mutatis
  - John Mount
  - Craig Reynolds
  - Imogenes
  - FORM
  - William Latham: Organic Art Mutator
  - Henry Rowley
  - Peter Kleiweg
  - Genetic Music
Additional Web Resources
Books
- Connections: The Geometric Bridge Between Art and Science Jay Kappraff
- Fragments of Infinity Ivars Peterson
- Godel, Escher, Bach: An Eternal Golden Braid Douglas R. Hofstadter
- Art & Physics Leonard Shlain
- The Visual Mind: Art and Mathematics Michele Emmer
Other Courses