10263
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Integer Torus Maps
Each point {x,y} in an integer grid of size n is joined to the point with coordinates obtained by iteratively applying the transformation Mod[{{a,b},{c,d}}.{x,y},n] the specified number of times.
Contributed by:
Stephen Wolfram
SNAPSHOTS
DETAILS
When the matrix {{a,b},{c,d}} is invertible, every point in the grid maps to a distinct point.
RELATED LINKS
Higher-dimensional generalizations [of iterated maps]
(
NKS|Online
)
PERMANENT CITATION
"
Integer Torus Maps
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/IntegerTorusMaps/
Contributed by:
Stephen Wolfram
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Integer Torus Maps Applied to Letterforms
Stephen Wolfram
State Transition Graphs for Integer Torus Maps
Stephen Wolfram
Trajectory of a Point in an Iterated Torus Map
Stephen Wolfram
Iterates of the Logistic Map in 3D
Stephen Wolfram
Cellular Automata as Mappings
Stephen Wolfram
Sensitive Dependence in Iterated Maps
Stephen Wolfram
Cellular Automaton State Transition Diagrams
Stephen Wolfram
Orbit Diagram of Two Coupled Logistic Maps
C. Pellicer-Lostao and R. Lopez-Ruiz
Variations of the Gingerbreadman Map
Erik Mahieu
Orbit Diagram of Two Coupled Logistic Maps with Delay
C. Pellicer-Lostao and R. Lopez-Ruiz (University of Zaragoza, Spain)
Related Topics
Chaos Theory
Discrete Models
Dynamical Systems Theory
High School Finite Mathematics
High School Mathematics
Visual Patterns
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+