DDLab is an interactive graphics program for research into the dynamics of finite binary networks, from Cellular Automata (CA) to random Boolean networks, including their attractor basins. The program is relevant to the study of complexity, emergent phenomena, neural computation and aspects of theoretical biology such as modelling gene regulatory networks. The results presented in (Wuensche 1992-1995) may be implemented with this program.
Versions of the program run on the following platforms: DOS-PC (vga and svga), UNIX/XWindows-Sun-Spark, and the Mac. This manual covers all three versions. The various versions function in essentially the same way, though aspects of the graphics presentation may be slightly different.
Using a flexible user interface, a network can be set up with any architecture ranging from regular CA (1d or 2d with periodic boundary conditions) on the one hand, and random Boolean networks (disordered CA) on the other. The latter have arbitrary connections, and rules which may be different at each site. The neighbourhood (or ``pseudo-neighbourhood``) size may be set from 1 to 9, and the network may have a mix of neighbourhood sizes.
The program is able to compute the global dynamics of networks as well as run the usual forward dynamics to show space-time patterns. For global dynamics the network is run ``backwards`` to generate a pattern's (or state's) predecessors and reconstruct its branching sub-tree of ancestor patterns. All ``garden of Eden'' states, the leaves of the sub-tree, may be disclosed. Sub-trees, basins of attraction or the entire basin of attraction field (referred to collectively as ``attractor basins``) can be displayed as a directed graph or set of graphs in real time, with many presentation options.
It can be argued that attractor basins represent the network's ``memory'' by the hierarchical categorisation of state-space. Each basin is categorised by its attractor and each sub-tree by its root. Learning/forgetting algorithms allow attaching/detaching sets of states as predecessors of a given state by automatically mutating rules or changing connections. This allows sculpting the basin of attraction field to approach a desired scheme of hierarchical categorisation. The attractor basins of ``random mappings'' (with or without various biases) can also be generated.
Whereas large systems sizes may be run forward to look at space-time patterns, or backwards to look at subtrees, much smaller sizes (say less than 18) are appropriate for the entire basin of attraction field given that state-space grows exponentially with system size. The program's upper limit for basin of attraction fields is 32; there is no limit for single basins or sub-trees. Larger sizes may be tried, but may impose unacceptable time, memory or display constraints. Sub-trees may be generated for much larger systems for rules having a low in-degree.
The network's parameters, and the graphics display and presentation options, can be very flexibly set, reviewed and altered. Changes can be made ``on the fly``, including mutations to rules, connections or current state. 2d networks (including the ``game of life'' (Conway 1982) or any mutation thereof) can be displayed as a space-time pattern in a 3d isometric projection.
Various quantitative, statistical and analytical measures and data on both forward dynamics and attractor basin topology are made available in DDLab, as well as various global parameters of rules and network architecture. These measures and data (mostly presented graphically) include the following:
The (or P*) parameter and the Z parameter.
The frequency of canalyzing ``genes'' and inputs. This can be set to any arbitrary level.
Various measures on forward dynamics such as pattern density, frozen islands, pattern difference between two networks*, the Derrida plot*, rule-table lookup frequency and entropy, and the variance of the entropy*, which allows ordered, complex and chaotic rules to be discriminated automatically *.
Various global measures on the topology of attractor basins including garden-of-Eden density and a histogram of in-degree frequency.
A scatter-plot of state-space.
(items marked * are not yet covered in the program reference #4)
The network architecture, states, data, and the screen image can be saved and loaded in a variety of tailor-made file formats.
#A1-10 gives a overview of the program. #1-3 give some ``quick start'' examples. These should be tried initially to get the flavour of the DDLab. #4-28 is a detailed reference manual relating to the DOS version of DDLab, and omitting a number of new functions - however this should provide an adequate guide until the manual is updated.
For further background on the attractor basins of CA and random Boolean networks, and their implications, refer to Wuensche (1992-1995), Kauffman (1993) and other references listed in #A10. DDLab is in the process of continual development. New features are being added in response to various research needs. Some aspects of this manual may be out of date or not applicable to particular platforms.