# Wator

Wator is a discrete simulation for modeling a simple predator-prey model . It was co-designed by Alexander K. Dewdney and David Wiseman and first published in the December 1984 issue of Scientific American magazine. In the German-speaking area it appeared in the special edition series Computer Kurzweil of the journal Spektrum der Wissenschaft , and later also in a book of the same name by the Spektrum akademischen Verlag.

## introduction

Excerpts from a Wator simulation. Fish are shown in green, sharks in blue.

A closed system is simulated, a hypothetical, toroidal " planet ", which Dewdney called Wa-Tor (derived from Water- Torus ). The toroidal shape of the planet was only chosen by Dewdney for practical reasons, since a simulation on a spherical surface would have been much more complex to program. 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 on Wa-Tor . The fish feed on plankton , which is available in any quantity and is therefore not explicitly considered. The sharks, on the other hand, only eat fish and are dependent on this food for survival.

## playing area

The playing field is divided into rows and columns. All opposite sides are connected torically . Each cell on the playing field can assume three states. She can:

• be covered with a shark.
• be topped with a fish.
• to be empty.

A color is assigned to each of the three states. In the picture on the right these are black for water, green for fish and blue for sharks. At the beginning of the simulation, a random starting population is placed on the playing field.

## Rules of the game

Each of the two species behaves according to clearly defined rules. An individual moving up out of the playing field will re-enter on the bottom and vice versa. The same goes for the horizontal direction.

### Rules for fish

• Each fish swims randomly on one of the four adjacent spaces, provided it is empty.
• Every fish has an age; If this age exceeds the "Breed Time", a new fish is born in an empty, adjacent field.

### Rules for sharks

• Sharks eat fish in adjacent fields.
• If a shark does not find a fish in an adjacent field, it swims randomly on one of the free, adjacent fields.

There are two different implementations for the reproduction of sharks:

• If a shark does not find a fish for a certain number of cycles, the "Shark Starve Time", the shark dies.
• Sharks reproduce in the same way as fish do; H. after the "Shark Breed Time" a new shark is born in a neighboring field.

The second implementation does not work with a time counter, but with energy points.

• For every cycle in which the shark does not find a fish, it loses one energy point.
• If the shark finds a fish, its energy is increased by the energy value of the fish.
• If the energy exceeds the value for the production of an offspring ("Breed Energy"), a new shark is born in an adjacent free field. The existing energy is evenly distributed between the old and new shark.

The simulation depends on 5 changeable parameters : the number of fish at the beginning, the number of sharks at the beginning, the Fish Breed Time, the Shark Breed Time and the Shark Starve Time. In the second implementation, the Shark Breed Time is replaced by the Shark Start Energy (energy points of the shark at the beginning), the Shark Breed Energy (energy that is required to produce offspring) and the Fish Energy (energy value of a fish).

In addition, the course of the simulation depends on the size of the planet, but this is taken for granted. The simulation can be seen as a game: the aim of the game is then to choose the starting parameters so that a stable equilibrium is created.

## Simulation process

Depending on the start parameters, there are different ways in which the simulation can develop:

• The sharks can become extinct and give free rein to the fish.
• The fish can become extinct, which will result in the sharks becoming extinct.
• A kind of equilibrium can arise in which the two populations limit each other. Most of the time this consists of periodic fluctuations in the populations. Most of the time, the amount of fish is reduced to a certain population, so that the shark population is reduced to a few specimens. This allows the fish population to grow again until the shark population can keep up with the growth spurt.

A very interesting process arises when the fish reproduction ("Fish Breed"), the shark reproduction ("Shark Breed") and the shark hunger ("Shark Starve") are all set to the value 1 (1 round = 1 time unit). After a short time, “fish fronts” form, which are systematically “pursued” by sharks. The number of both remains very stable, curiously, there are always more sharks than fish.

## literature

• Immo Diener (Ed.): Computer Kurzweil. Volume 2. Spectrum - Akademischer Verlag, Berlin 1992, ISBN 3-86025-030-2 .