9887
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
State Transition Diagrams for Modular Powers
Each point represents an integer, joined to the point representing the result of the modular power. The structure of the final "state transition diagram" varies greatly with both the multiplier and modulus.
Contributed by:
Stephen Wolfram
Based on a suggestion by:
Stan Wagon
With additional contributions by Robert Baillie
THINGS TO TRY
Slider Zoom
Automatic Animation
SNAPSHOTS
DETAILS
Mouse over points to see the integers to which they correspond. A number pointing to
means the number has no root for the given
.
Fermat's little theorem, Euler's theorem, quadratic residues and nonresidues, and other number theoretic phenomena are visible.
RELATED LINKS
State Networks for Systems of Limited Size
(
NKS|Online
)
Systems of Limited Size and Class 2 Behavior
(
NKS|Online
)
PERMANENT CITATION
"
State Transition Diagrams for Modular Powers
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/StateTransitionDiagramsForModularPowers/
Contributed by:
Stephen Wolfram
Based on a suggestion by:
Stan Wagon
With additional contributions by Robert Baillie
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
State Transition Diagrams for Modular Multiplication
Stephen Wolfram
State Transition Graphs for Integer Torus Maps
Stephen Wolfram
Divisibility Networks
Yifan Hu and Stephen Wolfram
Cellular Automaton State Transition Diagrams
Stephen Wolfram
Clustered Power-Law Networks
Seth J. Chandler
Networks for Basic Number Theoretic Functions
George Beck
Graph Detangling
Yifan Hu and Stephen Wolfram
Divisibility Graph
Don Goldberg
Lattice of Factors
Rob Morris and George Beck
PowerMod Is Eventually Periodic
Oleksandr Pavlyk
Related Topics
Finite State Machines
Networks
Number Theory
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+