Calculate and graphically display Lattice Dynamical Systems

Authored and Contributed by
Ronald Joe Record
Copyright 1993, 1994 Ronald Joe Record
The mathrec source code is freely redistributable. The author maintains binary distributions for Caldera OpenLinux 3.1, OpenServer, UnixWare 7 and Open UNIX 8. These distributions and the source code are available via:

Binary Distributions
OpenLinux/Open UNIX (no longer available)
UnixWare 7

Source Code Distributions
Source RPM (no longer available)
Gzip'd tar archive

Lds is an X11 client.

The lds program generates and displays a sequence of curves or cellular automata like figures which graphically represent the evolution of a Lattice Dynamical System (LDS). An LDS is an array of cells, each of which represents a dynamical system. Each cell is coupled to its nearest neighbors. The dynamical systems available in this software package are currently the logistic map, circle map and tent map. The state of each cell in the LDS is a real number in the unit interval. The evolution of the lattice is determined by an iteration thru the specified dynamic (e.g. the logistic equation) followed by a weighted averaging with its nearest neighbors.

Command line arguments and run-time keyboard input allow lds to simulate a wide variety of lattice dynamical systems. The user can specify the dynamic to be used, the non-linearity parameter, the strength of coupling, the initial conditions, the size of the array, the length of the run, whether and how to evolve connection strengths, and more. During the run, the display of the evolving LDS can either be CA-like with each generation being represented as a horizontal line evolving upward in the window or as points or a curve with X axis the lattice and Y-axis the cell states [0,1]. In addition, graphical display of cell states can be toggled between actual state and phase difference with left neighbor. A site histogram curve can also be displayed.

Lattice dynamical systems are also referred to as coupled map lattices.

The literature is sparse but includes the following excellent papers :

"Lyapunov Analysis and Information Flow in Coupled Map Lattices" by Kunihiko Kaneko, Physica 23D (1986) 436-447

"Spatiotemporal Chaos in One- and Two- Dimensional Coupled Map Lattices" by Kaneko

"Spatiotemporal Chaos and Noise" by Gottfried Mayer-Kress and Kaneko, J. Stat. Phys.(1988)

"Pattern Competition Intermittency and Selective Flicker Noise in Spatiotemporal Chaos" by Kaneko, Physics Letters A, V125, 1 (1987)

"Pattern Dynamics in Spatiotemporal Chaos" by Kaneko (1987)

"Phenomenology of Spatial-Temporal Chaos" by Jim Crutchfield and Kaneko, appearing as a chapter in "Directions in Chaos" edited by Hao Bai-lin, World Scientific Publishing (1987)

"Robust Space-Time Intermittency and 1/f Noise" by James Keeler and Doyne Farmer, Physica 23D (1986) 413-435

To build the lds binary, either use the Imakefile or the sample makefile - Makefile.std. To build with the Imakefile, first type "xmkmf" or "imake -DUseInstalled -I/usr/lib/X11/config" if your system doesn't have xmkmf. Then just type "make" and the lds binary will be built.

The manual pages can be formatted by typing "nroff -man > lds.doc"

To install lds, copy the lds binary to the desired location (the sample makefiles put it in /usr/local/bin) Copy the formatted man page to wherever you keep your local doc (i use /usr/local/man/cat1 for imaging software), then add that location to your MANPATH.
This program can be used to explore the largely unmapped terrain of the evolution of coupled map lattices. In that sense, it may assist in the construction of a phenomenology of such maps.
I have used this for years without harm.
Work Planned
manual page.
Execute any or all of the shell scripts provided in /usr/local/mathrec/lds.
Ideas, comments, additions, deletions, suggestions, bug reports, code review,... e-mail Ronald Record at