Wolfram Computation Meets Knowledge

Wolfram Summer School


Christopher Maes

Summer School

Class of 2003


At present Chris is pursuing his undergraduate degree at the Massachusetts Institute of Technology, majoring in Applied Mathematics and Computer Science. His interests are in functional programming, numerical analysis, nonlinear dynamics, complexity, and computer vision. While still in high school, Chris developed a contour based pattern recognition algorithm for identifying Western Painted Turtles. His current research is on multiple particle tracking in the Program in Atmospheres, Oceans and Climate under the Department of Earth, Atmospheric, and Planetary Sciences. When his hectic schedule at MIT allows, he enjoys spending time with the other members of Fort-Awesome, reading contemporary and modern literature, running and rock climbing.

Project: Complex Behavior in Digit Sequences produced with Simple Iterated Maps

Iterated maps operating on x and the representation of x in base b are studied. Particular attention is paid to the reversal addition map given by x_{n+1} = x_n + R(x_n,b) (where R(y,b) is the reversal of y in base b). Qualitiative classes of behavior similar to those in cellular automata are found in successive terms in the sequence. An algorithm for classifying unique sequences and determing the behavior of a sequence is presented. All simple maps are enumerated and those maps which produce complex behavior found. Carry propagation and depence on initial conditions are anaylzed. A conjecture on the maps which will yield complex behavior and the universality of these maps are discussed.

Favorite Three-Color Cellular Automaton

Rule Chosen: 6581808479559

Additional Information

Maes, C. “Complex Behavior in Digit Sequences Produced with Simple Iterated Maps.” Presentation at NKS 2004, Boston, MA, 2004. [abstract] [materials]