Wator

Wator is the name of a discrete simulation for the modeling of a simple predator-prey model. It was designed jointly by Alexander K. Dewdney and David Wiseman and 1984, first published in the December issue of Scientific American magazine. In the German -speaking world it was published in the special issues of the journal Computer Kurzweil of Scientific American, and later in a book of the same spectrum of academic publishing.

Introduction

Simulates a closed system, a hypothetical toroidal "planet" (derived from Water - Torus) called the Dewdney Wa -Tor. The toroidal shape of the planet was chosen by Dewdney only for practical reasons, because a simulation would have been considerably more complex to program on a spherical surface. The surface of this " planet " is completely covered by water, in which only two species, sharks and fish, exist. The model simulates the food chain to Wa -Tor. The fish feed on plankton, which is in any amounts available and therefore is not considered explicitly. The sharks, however, eat only fish and rely on this food to survive.

Playing surface

The playing field is divided into rows and columns. It all opposite sides are connected toric. Each cell of the playing field can have three states. You can:

• Be occupied with a shark.
• Be with a fish occupied.
• Be empty.

Each of the three states is assigned a color. In the picture, these are black for water, green for fish and blue shark. At the beginning of the simulation a random initial population is placed on the field.

Game rules

Each of the two species behaves according to clearly defined rules. An individual who moves up from the playing field, will join on the bottom again, and vice versa. The same applies to the horizontal direction.

Rules for fish

• Each fish swims randomly to one of four adjacent fields, if it is empty.
• Each fish has an age; exceeds this age the "Breed Time", so is born on an empty, adjacent field, a new fish.

Rules for sharks

• Sharks eat fish on adjacent fields.
• Find a shark any fish to an adjacent field, so he swims randomly on one of the free, the adjacent fields.

For the multiplication of sharks there are two different implementations:

• Find a shark for a certain number of cycles, the "Shark Starve Time", no fish, so dies the shark.
• Sharks reproduce exactly so forth like fish, ie after the "Shark Breed Time", a new shark is born on a neighboring field.

The second implementation does not use a timer but with power points.

• For each cycle, during which the shark is no fish, losing an energy point.
• Find the shark a fish, its energy is increased by the energy value of the fish.
• Exceeds the energy value for generating a progeny ( "Breed Energy" ), a new shark is born on an adjacent open field. The available energy is distributed equally between the old and new shark.

The simulation depends on five variable parameters: the number of fish at the beginning, the number of sharks in the beginning, the Fish Breed Time, the Time and the Shark Shark Breed Starve Time. In the second implementation, the Shark Breed Time by Shark Home Energy ( energy points of the shark at the beginning ), the Shark Breed Energy ( energy required to produce an offspring) and the Fish Energy ( energy value of a fish ) replaced.

In addition, the sequence of the simulation depends on the size of the planet, but this is assumed to be given. The simulation can be thought of as a game, the goal of the game is then the starting parameters to be chosen such that a stable equilibrium arises.

Simulation course

Depending on the starting parameters, there are various ways in which the simulation can develop:

• The sharks can die and let the fish run free.
• The fish can die out, which will entail extinction of sharks after themselves.
• It can be a kind of equilibrium arise in the limit, the two populations mutually exclusive. Most of this consists in the fact that it comes to periodic fluctuations in the populations. In most cases, reduces the amount of fish on a particular population, so that the shark population goes back to a few copies. This allows the fish population grow again until the shark population can meet the growth spurt.

A very interesting development arises when the fish propagation ( "Fish Breed" ), the Haivermehrung ( "Shark Breed" ) and the Haihunger ( "Shark Starve " ) are all set to the value 1 ( 1 lap = 1 time unit). After a short time form " fish fronts " which are " persecuted " by sharks systematically. The number of both remains very stable, oddly enough, there are more and more sharks than fish.