1. A system that will spontaneously increase its organization as it is moved further from equilibrium with respect to distributions of conserved quantities. In this model, the multiplicative product of the population of numbers is conserved. The distance from equilibrium is manipulatable by a control parameter that defines the gradient from the source to the sink.
2. As simple a model as possible to explore self-organizing autocatalytic networks and dissipative structures.
3. A system that will spontaneously decrease its organization as the control parameter is moved closer to equilibrium.
4. Mechanisms to track economic transactions through the system and perform double-entry accounting for each agent.
5. Ability to tag matter as it moves through the system to measure residence time which will serve as a measure of complexity in the system.
6. Create a visualization that allows the user to get the feel of self-organizing structures emerging to dissipate gradients.

Figure 1: diagram of WebEconomy interactions

Numbers: Are consumed and produced by agents. Prime numbers are the prime factors of production at the source. Intermediate products are created as the product of 2 or more numbers. Decomposition of products is performed through factoring.

Recipe: Specifies materials on one side of the equation and products on the other. Like a chemical reaction, this recipe can be performed in the reverse direction if there is a low concentration on the materials side and high relative concentration on the product side. Each recipe has a time cost to perform.

Example: 3 * 6 = 18. The agent can either take in one 3 and one 6 from the environment and produce one 18, or take in one 18 and produce one 3 and one 6.

Autocatalytic Sets: A chain of products and materials that form a closed loop.

Example: in Figure 1 agent1, agent2 and agent3 form an auto-catalytic set involving the numbers 2, 3, 6, 9, and 18. Overall, this cycle consumes 3s and produces 9s (which are then consumed by the sink in this example). Consuming 3s and producing 9s can be seen as the function of this auto-catalytic set, and defines its functional closure. Other auto-catalytic arrangements can be produces that have the same function but a different structure.

1. Identifying autocatalytic sets

Autocatalytic sets may be identified as cycles in the transactions graphs which can be considered similar to chemical reaction graphs. The model will include the ability to search the network for cycles that form a functional closure. An alternative technique may include a mechanism to identify symmetry breaks in temporal activities in the system. Autocatalytic sets, by definition will react at greater rates given sufficient inputs.

• Each agent has a list of recipes which constitute their knowledge.
• These recipes contain numbers specifying what they need.
• Agents have a store of numbers, transacted from the embedded market.
• Agents do not have exogenously defined preferences. They learn to value numbers and recipes.

Agents can be represented as nodes in a graph. Edges are drawn from an agent whose MAKE matches another agent's USE (In the case of reversible recipes MAKE and USE may be the same set). Finding closed cycles in this graph specifies and autocatalytic set in the graph.

2. Determining which formulas an agent has knowledge of

-Formulas are also a part of the "environmental market"
-Unlike numbers, when another agent "buys" and "uses" another agent's formula it is not used up.
-"Base formulas" are seeded into the environment by the source along with prime numbers. Alternative mechanism of innovation can be used where agents try to factor needs that they have encountered. Efforts to create new factorings or recipes, should come at a cost.

3. Creating new prime numbers and new recipes

-New formulas are created by genetic operations performed on existing formulas by agents.
-Crossover example: (3 * 4 = 12) cross (5 * 6 = 30) ==> (5 * 4 = 20)
crossover creates new products using existing factors
-Mutation example: (3 * 4 = 12) ==> (2 * 6 = 12)
mutation uses new factors to create an existing product

-New prime numbers can be created by identifying autocatalytic sets and labeling them with an new prime number. These sets can then be used as if it were that prime number.

4. Adding/Removing agents from the system

-New agents appear when there is a large quantity of a specific factor (number) and try to acquire/create a formula that uses that number.
-Agents leave the system when they can not maintain enough profit to maintain themselves or participate in an autocatalytic set in which they are maintained.