Continuous Predator/Prey/Grass simulation using WebGL

Tools

Place Plant

Place Herbivore

Place Carnivore

Place Meteor

To use a tool, click on it and then click on the appropriate place on the world.

World Dynamics

c_{r}

: Carnivore Eat rate bodyweight per second in presence of infinite herbivores

c_{b}

: Herbivore Eat rate bodyweight per second in presence of infinite plants

c_{g}

: Plant Growth rate times existing weight per second in presence of infinite space and fertility

c_{f}

: Fertility Change rate proportion per second towards plant density

m_{r}

: Carnivore Metabolism rate bodyweight per second lost

m_{b}

: Herbivore Metabolism rate bodyweight per second lost

d_{r}

: Carnivore Diffusion rate proportion per second

d_{b}

: Herbivore Diffusion rate proportion per second

d_{g}

: Plant Diffusion rate proportion per second

Display Infertile color Fertile color
Show Life proportion of color coming from life (remainder from ground fertility)
Warp (integer) iterations per display frame
FPS : ???

What is going on

There is grass growing (green), herbivores eating the grass (blue), and carnivores eating the predators (red). Each has a density between 0 and 1, which controls the intensity of the corresponding color. There is also soil fertility, which goes up when there is lots of grass around and goes down when there is not. Plants, herbivores and carnivores will diffuse into adjacent regions. Note that is possible for a species to die out. More plants, herbivores and carnivores may be placed by act of god (you) using the tools above. You can also smite the ungodly if you wish with rocks from heaven.

The actual equations used depend upon the constants listed under world dynamics.

$f$ is the soil fertility (at one place) (0-1)
$g$ is the vegetation [grass] density (0-1)
$b$ is the herbivore [bison] density (0-1)
$r$ is the carnivore [rabbits, man eating variety] density (0-1)
$F$ is the mean soil fertility in the four orthogonally adjacent pixels to the current place. Similarly for $G$ , $B$ and $R$
$d_{f}$ , $d_{g}$ , $d_{b}$ , $d_{r}$ are diffusion rates. Currently $d_{f} = 0$

The world then evolves according to a discretized version of the following equations, which each variable clamped to the range 0-1:

$e_{g} = g b c_{b}$ (rate at which herbivores eat vegetation)
$e_{b} = b r c_{r}$ (rate at which carnivores eat herbivores)
$\frac{d}{dt} g = d_{g} (G - g) + g (1 - g) c_{g} f - e_{g}$
$\frac{d}{dt} b = d_{b} (B - b) + e_{g} - e_{b} - m_{b}$
$\frac{d}{dt} r = d_{r} (R - r) + e_{b} - m_{r}$
$\frac{d}{dt} f = d_{f} (F - f) + c_{f} (b - f)$