E42: DISCRETE DYNAMIC SYSTEMS
SIMULATION TOOLS

E42 is a Software Suite that generates random graphs, small world, ordered, and scale free networks in the form of NK Boolean Systems. These Booleans networks generate emergent Landscapes.

E42 has tools for analyzing both the characteristics of static networks (e.g., distributions of connections, log-log slopes of connection distribution) and the dynamics of emergent Landscapes (e.g., finding and archiving Basins of Attraction (Attractors, Tributaries), Dynamic Motion of Attractor Cycles, Derivatives of Attractor Cycles, Perceptual Categories of Attractors based on Derivatives, Phase Portraits, and so on.) These analyses are performed on saved files by tools internal to the Core E42 program or by a series of special analysis tools such as MetaTAO and Symmetry Group Search.

Theory, implications, and publications can be found here.

Designers: Tom Malloy, Gary Jensen, & Jonathan Butner
Programmers: Gary Jensen, Tim Song, Chase Dickerson, Felix Lau

All Code is Open. Copyright: GPL

 
BELOW: On the left are two examples of Networks Types: (A) Random Graph and (B) Scale Free. Notice the branching fractal-like structure of Ordered Random (scale-free) network. Both networks are among the various types of networks that can be generated by E42. The Emergent Landscape shown to the right is unrelated to either network and is included to make the distinction between a static network and the dynamics that emerge when something flows across a network (information, electicity, social communication, and so on).
A

A 100 Node Random Graph Network. Blue squares represent nodes; red lines represent connections.

: ==>

A Dynamic
Landscape Emerges from a Network

: ==>

Representation of an Emergent Lanscape with three attractors (fitness peaks) --From Wikipedia

B

A 100 Node Ordered Network with a scale-free fractal structure. Blue circles represent Nodes.

 

ABOVE: Graphic representation of the dynamics of one attractor cycle on an emergent landscape. The cycle repeats endlessly. Nodes are on the Vertical Axis and Time (Iteration) is on the Horizontal Axis. Twenty-two Nodes are shown (counted on the vertical axis). Each Node can be ON or OFF. A BLACK Node-by-Iteration cell indicates the cell is ON. A WHITE cell indicates that that paricular Node is OFF on that particular Iteration. A single column of BLACK and WHITE cells shows the state of the system (which nodes are ON and which are OFF) at a particular moment i time. Each row shows the ON-OFF pattern of one node across time. This representation is called an Historical Trace because it shows the ON-OFF pattern of all the nodes across time and makes the attractor's dynamics easy to perceive. This attractor cycles every 24 iterations.

 

E42 Classic : NK Boolean Simulation Software
Version 1.3 2008-10-27
(requires java plugin 1.4 or higher)
(This is a WebStart version) FILE TYPE: e42in

E42 Classic software generates only Random Graphs Networks. These (static) networks generate emergent (dynamic) Boolean Landscapes consisting of many basins of attration. E42 Classic has an extensive suite tools to analyze the dynamics of the Landscape that emerges from the network.

E42 is a simulation tool for creating Boolean Discrete Dynamic Systems in the form of Networks consisting of N nodes, each of which has K inputs. For fuller explanations and research results go here. E42 Version 1.2 and higher calculates derivatives of attractors (TAO Tool), sorts attractor patterns into categories based on derivatives, and produces dynamic form effects as a way of capturing Landscape dynamics. E42 version 1.2.9 was completed 2008-10-27. Minor changes since then have resulted in version 1.3. (stat/E42/index.html)

 

 

E42 Plus : NK Boolean Simulation Software with Network Builder enhancements
Version 1.83. May 18, 2011. (This is a Webstart version) FILE TYPE: .XML

E42 Plus can generate Boolean Networks in the form of Random Graphs, Ordered Networks, Networks with Preferential Ponnectivity, and combinations of ordered and perferential networks. Thus it operationalizes the distinctions made by Barabasi, Watts, and others (Small Worlds, Scale Free Networks, etc).

E42 Plus incorporates Network Builder directily into E42 to faciliatate the investigation of random graphs, small world, preferential attachment and other network generating rules. This allows E42 Classic's suite of tools for analyzing Landscape dynamics to brought to bear upon a large variety of network types. (stat/E42_Network-Builder/E42_Network-Builder.jar)

E42 Plus has a file type that is incompatible with E42 Classic.

 

 
Network_Builder: Network Builder mimics the E42 Core but lacks E42's major features and tools. Network builder adds options that allow investigation of random graphs, small world, ordered networks, preferential networks, and thus can produce scale free networks. Network Builder graphs the output distribution connections as well as calculating the the log-log slope of the output distribution. FILE TYPE: e42in and XML (stat/E42_Network-Builder/Old/E42_Network-builder.jar)
 
 
Boolean Phase Portrait : Meta-TAO Classic: For e42in files. Meta-TAO is a tool for exploring higher order relations among Boolean Derivatives. It is important in finding symmetry groups among attractors on a Landscape but requires tedious visual inspection to do so. (requires java plugin 1.4 ) INPUT: e42in FILE TYPES (stat/meta-TAO/Meta-TAO Original/Meta-TAO-jar)
 
Boolean Phase Portrait : Meta-TAO Plus: For .XML files Meta-TAO Plus take files from E42 Plus with Network Builder Enhancements This functions in the same way as Meta-TAO Classic except that upon opening it can convert an XML filetype to a serialized object and analyze it. (stat/Meta-Tao_2_XML/Meta-TAO.jar)

 

 
UBER-TAO Classic : A TAO-Meta-TAO Attractor Search Tool (Folder: Group_Finder) This program can only input the e42in file type.This program compares (XOR) every TAO matrice and/or Meta-TAO matrix looking for a comparision that generates one of the known attractor matrices. This tool starts with one target attractor and shows how transforms of that attractor can find other attractors. This tool is essential for finding symmetry groups among attractors on a landscape since it automates the search for such groupls It is slower than but more complete than Symmetry Group Finder Tool. INPUT: e42in FILE TYPES (stat/Group_Finder/index.html)
SYMMETRY SEARCH PLUS (formerly: UBER-TAO Plus : A TAO-Meta-TAO Attractor Search Tool with a filetype Converter that allows analysis of networks generated E42 Plus (which has an XML file type). (stat/Symmetry-Search/symmetrySearch.jar)
Symmetry Group-Finder LITE : This tools finds symmetry groups based on TAO and Meta-TAO analysis. Related to but less rigorous in its search than is the UBER-TAO TAO-Meta-TAO Search Tool. Runs faster than TAO-MetaTAO Tool. INPUT: e42in FILE TYPES (stat/Group_Finder/index.html)
 
 
Sierpinski Wrapper Tool. This tool does not need to import E42 files. This program wraps a Sierpinski Gasket around manifolds of various circumferences. The circumference represents attractor cycle length, L. The user can input L and also input the number of rows, R, in the Sierpinski Gasket. The output is an image of the S-Wrap transform. This shows that the S-Wrap transform produces a form of symmetry that generates the derivatives of attractor cycles on a Boolean Landscape. (stat/Sierpinski_Wrapper/index.html)
Minimum Number of Sierpinski Gaskets Tool. This tool will take any node row vector and find the all possible combinations of overlapping Sierpinski Gaskets that can reproduce that node's ON-OFF pattern to recreate that node pattern. From the output it is possible to infer the minimum number of Gaskets to produce the node row vector pattern. This may be a measure of Complexity. (stat/Sierpinski_Searcher/index.html)
Normalized Attractor Archive Converter
This tool creates attractor archives that are rational. It converts basin numbers created by TAO to Basin numbers that are based on the lowest Boolean value (of the rotated basin). [TAO finds basins pseudo-randomly and assigns a number to the basin in the Basin Archive in the order of its discovering the basin. The Basin Converter tool goes through the archive and renumbers the basins with a number based on the lowest Binary Value of state vectors. . INPUT: e42in FILE TYPES (stat/Basin_Converter/index.html)
 
 
New Media Executable Creator
This tool allows you to save an instance of an E42 eefer as a Windows executable Applet file. This is essential when you want to capture a specific phenomenon found in E42 (which seldom returns to she same phenomenon once it has been perturbed). INPUT: e42in FILE TYPES
Vector Converter
Converts a RowXColumn table (of 0's and 1's) into and E42 file. For example a RxC table can become a Boolean landscape (as if generated by an eefer) that has R attractors each with only 1 node and each with cycle length, L = C. After this conversion we can input the artificial Boolean landscape into Meta-TAO or into the TAO-Meta-TAO Basin Search Tool. We can also transpose the RxC table so that we get an artificial landscape with R attractors each of L=1. (stat/Vector_Converter/index.html)
 
Classic Apparent Motion Applets
Four Types Classic Apparent Motion (stat/dynamic_systems/Content/examples/Apparent_Motion?motion.html)
Apparent Motion in Random Dot Displays (stat/dynamic_systems/Apparent_Motion?randomDots.html)
 
 
Dynamic Form Analysis Tool This tool is in early development. It is being used to decompose complex patterns humans perceive in certain dyanamic forms. Currently this tool is nearly abandoned software. (requires java plugin 1.4 )
 
Tom's United List of Web Lectures Fall 2010
 
 

Logistic Equation (Y = aX(1-X) & Chaos Applet
This is an applet that runs the logistic equation. No Instructions. Looks bleak when you open it but just choose a "fractal". If you're into the logistic map the options will give you stuff you want (the parabola, time series, sensitive dependence through comparing two initial values of X, Fiegenbaum Plot) for the purposes of demonstration and teaching.
(stat/dynamic_systems/Content/chaos/index.html)

Hysteresis Applet
This is an applet that creates a bifurcated potential well. A red ball run down into the well. Controls let you demonstrate hysteresis. . No Instructions. Looks bleak when you open it but just choose a "Tool". If you're into hysteresis you'll probably figure out how to run the controls. Main thing to know: drag the purple square at the bottom right or left to move the ball up the sides of the well. Then play with all the controls. One of the controls is the ball's "stickiness" or friction which controls how fast it falls and therefore its momentum.
stat/dynamic_systems/Content/hysteresis/hysteresis.html)

 

Conway's Game of Life
This Applet uses E42 as an interface. E42 is a more general system than Cellular Automata; therefore we can build CA in the E42 (with some limitations). This applet uses E42 to generate one example of Conway's famous cellular automaton, Life. It is a demonstration interface and does not allow you to change the rules of Life. You can however, either globally or cell by cell, adjust which cells are on and off. Because this is an New Media executable, you cannot program it they way you can program E42. But it is a fun example of the Game of Life.
(stat/dynamic_systems/Content/examples/LIFE/html/index.html)

 
OLDER VERSIONS OF E42
 
E42 version0.9 subversion5.1 (3/3/302) folder: stat/testing...
E42: Discrete Dynamic Systems MODELER v1.29 (10/31/2006) (E42/olde versions)

TAO Tool: The Flow Change across Time (requires java plugin 1.4 ) Version 2
TAO is a tool for examining change over time in a Boolean Dynamic System. It is epistemologically grounded in the idea that the fundamental process of knowing is detecting differences. For fuller explanations and research results go here. stat/testing...

 

RELATED TOPICS

Other Open Source Software by Tom Malloy and Gary Jensen

Stat Sampler: Links to interactive, online tools for teaching and learning statistics

 
Psy 3000 | The Most Innovative Online Statistics Course on the Web
Open Learning Management System: Open-code tools for teaching online (no longer supported
Link to Theoretical Applications of E42 Simulation Tools
Web Pages Addressing Theoretical Issues in Discrete Dynamic Systems and
Human Epistemology
 
SPECIALIZED TOOLS
(no longer generally available)
Webapps E42 (requires java plugin 1.4 )
Webapps TAO (requires java plugin 1.4 )
Webapps Game Of Life (requires java plugin 1.4 )
 
old Webapps E42 (requires java plugin 1.4 )
old Webapps TAO (requires java plugin 1.4 )
 
Swarm Search (requires java plugin 1.4 ) STAT/TESTING...
Basin Networks (requires java plugin 1.4 ) STAT/TESTING...
e42 Evolution v1 (requires java plugin 1.4 )
e42 Evolution v2 (requires java plugin 1.4 ) STAT/TESTING...
Order Checker 1.1(requires java plugin 1.4 ) STAT/TESTING..

DISCLAIMERS: *** This is an active research area. ***Software is being updated on a daily basis so menu structure, features, etc. change constantly. ***We build with the latest Java version available, so the latest Java plugin is required. ***Interfaces are designed to answer specific research questions and so are not usually intuitive and simple. ***Documentation is nearly non-existent, and where there is documentation, it lags behind the constant software changes. ***We are very happy to communicate with you about these tools and provide you with information that allows you to use the software to demonstrate many dynamic system phenomena and to answer your own research questions.

CONTACT: To get information that allows you use this software more easily, contact Tom Malloy at malloy@psych.utah.edu

The following applets are poorly developed:
Cellular Automaton v1.0 (requires java plugin 1.4 ) STAT/TESTING...
Chaos Frame (requires java plugin 1.4 ) STAT/TESTING...
Virtual World maze v0.9.3 (requires java plugin) stat/maze/virutalworld3
Regression Lazar v1.0 dynmaic systems / content examples...