What is the Chaos Game Representation?

Chaos Game Representation (CGR) is a method of converting a long one-dimensional sequence, e.g. English text or genetic sequences, into a graphical form. It's essentially the application of non-random input to an iterated function system, and was developed by H. Joel Jeffrey.

New CGRs

These CGRs are based on an alphabet containing ASCII characters from code 32 through 126, which consists of the alphabet in upper and lower case and punctuation. The characters are arranged in a circle, with consecutive characters about 90 degrees apart.

[Digits 0-9, uniform]

Random digits 0-9 with a uniform distribution. The square shape is due to the digits being clustered in four places 90 degrees apart on the circle.

[Digits 0-9, 0-4 2x as likely]

Random digits 0-9, non-uniform distribution; Digits 0-4 are twice as likely as 5-9.

[Lisp source code]

Lisp source code. Lots of dashes, semicolons, parentheses and spaces.

[C source code]

C source code.

[Email text]

Email text.

[Random text]

Random text, letters [A-Za-z] and spaces, with spaces making up one tenth of the text.

[Random text]

Random text, letters [A-Za-z] and spaces, spaces comprising one third of the text.

[Random text]

Random text, letters [A-Za-z] and spaces, where spaces make up two thirds of the text.


Old CGRs

These CGRs folded their input alphabet into only 4 characters, arranged at the vertices of a square--which was enough to distinguish highly structured input from unstructured input.

[Digits 0-3, uniform] [Lisp source code]
Random digits 0-3, uniform distribution

Lisp source

[C++ source code] [Email text]
C++ source code

Email folder text

Related Links


John Wiseman / wiseman@inetmi.com
July 12, 1998