CALResCo Software Pages

ALIFE WITH DAWKS V1.0

A simple Artificial Life Framework populated with plants and an animal lifeform called the Dawk. Dawks move randomly, eat plants and each other, mate given the opportunity and eventually die of starvation or poison. This simulation contains no intelligence, no genes, no mutation. Nothing except the random behaviour of survival machines, yet shows the self-organizing behaviour of more complex systems. It is designed so as to be easily modified by the user to add more detailed features if required. The user can enter initial Dawk and food numbers, mating and food energies, food growth rate and poison numbers or switch on a pollution mode based on Dawk numbers.

ORDER FROM CHAOS V1.1

Prompts for a dimension between 3 and 100 and a move %. A start point is moved towards a randomly selected point by the specified amount. This repeats continually. That's really all there is to it ! Strangely some pretty complex patterns occur even for such a simple shift rule (including the Sierpinski Triangle). Try the 'Chaos Game' for yourself...

CHIRIKOV MAPPING V1.1

This is a chaotic map. An initially almost circular display will escape with time and cover the screen with intricate patterns and attractors. Formula is shown on the screen. User can zoom into the display and vary the parameters. Like all chaotic systems, sensitivity to initial conditions can generate large effects on the image for small modifications to the parameters.

BOOLEAN NETWORKS V1.5

This program is based on a matrix of 8100 logic gates, arranged in a 90 by 90 square. Each gate is two input of which there are 16 possible truth tables. The program allows the gate type to be chosen or assigned randomly from the available types. The two inputs for each are then assigned randomly to the output of another gate. Once started, each gate determines its input states and switches the output according to its logic function. This happens in parallel across all gates. The cycle is repeated as often as the user allows.

If a gate settles into a permanent on or off state (a fixed attractor) it is coloured white or black accordingly - dead states. If a gate cycles on/off at every change it is coloured blue - 50% probability of being in either state. All other gate outputs are evaluated in time to determine what percentage of the time they are on and coloured accordingly. For example a gate that only switches on once in every 5 cycles will show the 20% probability colour. Complex patterns are shown if gates enter a regular firing sequence (as part of a circuit). This display is somewhat crude but is the only way I've found of displaying what is happening without printing out some 8100 graphs ! An option to toggle the colour of probability 1 to black (same as probability 0) now makes it easier to see the structure.

You can select an individual logic gate for all the matrix, or allow the program to assign one randomly. You can also restrict the choice to a smaller number of gates -6 for example chooses from the first 6 gate types only. While running you may perturb at random the gate types to see the stability of the pattern.

The gates are listed in the rough order in which they lead to long attractors. The early gates change states easily, normally tending to give a chaotic display. The later gates tend to lock into fixed patterns with poor results. By chosing a suitable number the chaotic tendancy can be damped and perhaps order found.

result = expression1 boolean-operator expression2

     boolean-operator    Any of the following Boolean operators:

        NOT                 Bit-wise complement
        AND                 Conjunction
        OR                  Disjunction (inclusive "or")
        XOR                 Exclusive "or"
        EQV                 Equivalence
        IMP                 Implication
        IF                  IF  

    Each operator returns results as indicated in the following truth
     table. 1 is true ; 0 is false:

A Input  B Input XOR EQV NA NB A  B NOR NAND NIF IMP NIMP IF OR AND 0 1  
=======  ======= === === == == == = === ==== === === ==== == == === = =
0        0        0   1  1  1  0  0  1   1   0   1   0    1  0   0  0 1
0        1        1   0  1  0  0  1  0   1   1   1   0    0  1   0  0 1
1        0        1   0  0  1  1  0  0   1   0   0   1    1  1   0  0 1
1        1        0   1  0  0  1  1  0   0   0   1   0    1  1   1  0 1
                 ----------------------------------------------------------
Rule (in Hex)     6   9  3  5  C  A  1   7   2   B   4    D  E   8  0 F

For this system NA and NB are NOTs whose input is just the A or B assigned input. NAND, NOR, NIMP, NIF are NOTed AND, OR, IMP and IF. EQV is NOT XOR To complete the line up we have 1 and 0 which are input independent barriers.

MID NETWORK V1.1

This is the same principle as BOOLNET except that the matrix is only 729 gates (27x27). This speeds up the cycle by a factor of 10 and allows the dynamics of changing gates and perturbations to be seen more clearly.

SMALL NETWORK V1.2

This is the same principle as BOOLNET except that the matrix is only 81 gates (9x9). This speeds up the cycle by a factor of 100 and allows the dynamics of changing gates and perturbations to be seen clearly. An additional display of the wiring is provided. Perturbations are changed to affect the outputs only, system wiring and rules are maintained constant.

VARIABLE NETWORK V1.0

In this generalization of the Boolean Network the user can specify directly the network size, from 3x3 to 90x90, along with connectivity distance. The same design can then be run many times with random setups. Options to overlay the wiring of any network, to mutate states, links or gates and to vary the cycle speed are made available.

ATTRACTOR MAPS V3.0

This is again the same principle as BOOLNET except that here the matrix is only 9 gates (3x3). An additional detailed display of the wiring is provided. The main feature of this program however is the ability to display the state map of the network. Even with only 9 gates we have 512 possible states of the network. These are displayed as a matrix, 32 horizontal by 16 vertical steps. Choosing the attractor option plots a box for each state entered and a line connecting them. In this way a map of the attractor basin can be plotted and the attractor cycle identified. If a state returns to itself (a point attractor) then the box is shown with a small center dot.

This is the same principle as ATTRACT but the program defaults here to an asychronous update mode where only one random gate is updated on each time step. Additionally the networks can be rerun with randomised parameters without further parameter entry, speeding the search for interesting configurations of transient attractors.

PHASE PORTRAIT MAPS V1.2

An addition to the Attract program, based on the same 3x3 matrix. This program analyses all 512 initial states of the network and displays a coded picture of all the attractors present in the network with their lengths and minimum states. This allows the arrangement of attractors and their relationship to gate outputs to be visualised, showing the effect of each of the gates on the relevant attractors.

SELF-ORGANISED CRITICALITY V1.4

This also maps to a 90 x 90 matrix of cells, but in this case each cell is a simple heap of units. The system generates new units one at a time and drops them onto the matrix. Once a cell contains 4 units they then flow from that cell to the surrounding 4 cells (horizontal and vertical) adding one to each. Gradually the matrix fills up and the knock on effect of filled cells then filling neighbours and so on causes avalanches or cascades to take place over many different scales. Once such an avalanche exceeds in size the total number of cells we have reached self-organised criticality under my definition, loops form in the system. Past the edges of the map the units disappear and are lost from the system. An option is given to flow units at random rather than symmetrically.

This program shows that even for unconnected systems undergoing very simple rules self-organisation can occur once they are pushed from equilibrium. The time required for this to happen depends on the distribution density but can be very quick for the drip feed option. The program gives good feel for the time dynamics of these systems, even on a slow processor. The behaviour shows the power law distribution of perturbations typical in systems at the edge of chaos - too little stress gradually builds up, too much collapses back down, the system automatically balances itself at the critical point or phase boundary.

LOTKA-VOLTERRA MODEL V1.1

Somewhat different, this simply graphs in time the co-evolution of two populations following the equations designed by Lotka and Volterra.

Each equation has a population A or B, a growth rate Ga or Gb, a death rate Da or Db and a coupling rate Ca or Cb.

A population growth of 10 means an increase of 10% a cycle, but it will also die out at some rate eg 0.1 allows 0.1% to die each cycle. The coupling is the effect on population A of B, and on B of A.

The standard model assumes A is the prey, B the predator. So the coupling for A is negative (B eats it!) and reduces the population. Similarly the coupling for B is positive (A provides food) and B will increase. Depending upon parameters the system can settle, oscillate or go chaotic. The default looks to cycle evenly but does in fact become wildly erratic in time.

Alternative models are possible with the same formulae. Both couplings can be made negative - simulating an arms race, or both can be positive - simulating co-operation, mutual benefit or symbiosis.

AGENT NETWORK V1.0

A fully functional version is currently under development, but many options are currently available as an ongoing preview in four types:

General Net

This simulates a set of agents connected with a specified number of links in either symmetrical or small-world arrangements. The network is generated randomly to model many stochastic 'encounter' scenarios. The links can be 1-way or 2-way, they can be dynamically added, deleted or rearranged. Connections can prove to be multiple on any link (strength related, as in neural nets) or single. Displays of the layout by link strength or distance are possible, links going from one side of the (wraparounded) display can be shown or hidden (they are dotted if they exceed the specified distance). Wiring can be displayed or hidden. Initial display shows the strength of the links and nodes in terms of connections. The node display dynamics changes as the network is asked to evolve (in one of four current modes).

Synergic Net