Different centered symmetric patterns can be seen splitting each cell of a binary
matrix into four blocks, resulting in a
matrix. There are
different possible patterns (combinations). It is possible to apply the rules to a hexagonal image too.
Daniel de Souza Carvalho
Based on a program by:
Ed Pegg Jr
Each individual cell of nine blocks
is divided into four new blocks, with 16 possibilities:
Neighbors: those are the blocks side by side with the central cell
(N, E, S, W)
Corners: those are the blocks at each corner
(NW, NE, SW, SE)
Center: the cell in the middle
The same data source (the matrix) and rules are used to plot the hexagonal view; the only difference is in how the data is presented.
Inspired by: J. Tarbell, "
Breath of Complexity
." (January 3, 2007).
Substitution Systems and Fractals
Daniel de Souza Carvalho
Wolfram Demonstrations Project
Published: January 4, 2008
Embed Interactive Demonstration
More details »
Download Demonstration as CDF »
Download Author Code »
More by Author
Rotating Substitution Systems
Evolution of Rotating Substitution Systems in 3D
Substitution Systems for Elements of Two Kinds
Neighbor-Dependent Substitution Systems of Two Kinds
Sequential Substitution Systems
Multicolor Neighbor-Dependent Substitution Systems
Cyclic Tag Systems
Two-Dimensional Neighbor-Dependent Substitution Systems
Sequential Substitution Networks
NKS / Wolfram Science
High School Computer Science
Browse all topics
The #1 tool for creating Demonstrations
and anything technical.
Explore anything with the first
computational knowledge engine.
The web's most extensive
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
STEM Initiative »
Programs & resources for
educators, schools & students.
Join the initiative for modernizing
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
© 2017 Wolfram Demonstrations Project & Contributors |
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