Biotopia is a simple Artificial Life Simulator inspired in a program of the same name created by Anthony Liekens (version 2.0 released in 1995).

It works by letting creatures live in a simulated environment, where there's a competition for food and reproduction. Because of that competition we can observe a statistics tendency of complexity increase and adaptation.

usage: biotopia.py [-h] [--width WIDTH] [--height HEIGHT]
                   [--ancestors-energy ENERGY] [--offspring-energy ENERGY]
                   [--energy-loss ENERGY] [--energy-gain ENERGY]
                   [--start-food AMOUNT] [--start-keys AMOUNT]
                   [--start-population AMOUNT]
                   [--mutation-probability PROPORTION] [--chart-update CYCLES]
                   [--wrap-vertically] [--wrap-horizontally] [--auto-restart]

Biotopia - The Artificial Life Simulator

optional arguments:
  -h, --help            show this help message and exit
  --width WIDTH, -wd WIDTH
                        the simulation environment width
  --height HEIGHT, -ht HEIGHT
                        the simulation environment height
  --ancestors-energy ENERGY, -a ENERGY
                        the amount of energy the ancestors starts with
  --offspring-energy ENERGY, -o ENERGY
                        at each reproduction, the amount of energy the
                        offspring starts with
  --energy-loss ENERGY, -l ENERGY
                        the quantity of energy lost at each creature's cycle
  --energy-gain ENERGY, -g ENERGY
                        the quantity of energy gain at each food eat
  --start-food AMOUNT, -f AMOUNT
                        the amount of food the simulation's environment starts
                        with
  --start-keys AMOUNT, -k AMOUNT
                        the amount of key particles the simulation's
                        environment starts with
  --start-population AMOUNT, -p AMOUNT
                        The number of ancestors the simulation starts with
  --mutation-probability PROPORTION, -m PROPORTION
                        The chance of random mutation at each reproduction
  --chart-update CYCLES, -c CYCLES
                        Update the population/keys chart period
  --wrap-vertically, -wv
                        Whether or not to wrap the environment vertically
  --wrap-horizontally, -wh
                        Whether or not to wrap the environment horizontally
  --auto-restart, -r    Whether or not to restart simulation if population
                        reaches zero

• Click over the environment: zoom area.
• space: toggle pause simulation.
• r: restart simulation.
• d: toggle debug mode (show nearest creature energy and age, and some of the best creatures).
• h: toggle horizontal wrapping.
• v: toggle vertical wrapping.

Creatures, in this simulator, are simple beings with a multi-cellular structure. The very arrangement of its cells determines both its movement throughout the world, as well as its capacity of eating and reproduce.

To live, each creature looses energy, therefore, they must eat to keep up energy amount bigger than zero. If it ever reaches zero, the creature dies and its transformed into food for other creatures to consume.

Reproduction is assexual by means of self-replication, and have a change of random mutation (which means a single change in its structure). Creatures do not interact directly with each other.

There are two resources in the environment, represented as particles (pixels dots) scattered all over the place. These are:

• food - dark green pixels. They provide energy to the creature.
• key particles - dark yellow pixels. They are the only source of reproduction.

Each creature is born with a limited amount of energy, and at each simulation cycle, this energy is decreased by a fixed amount (default is 1). When the creature's energy reaches zero, it dies.

In order to rise its energy level, the creature must walk over the space and "eat" the food particles (dark green). Upon eating, the food particle disappears from the environment, and it's added a certain amount of energy (default 10) to the creature.

When death occurs (energy reaches zero) the creature stops operating and its structure is transformed in food particles and one key particle, which can be consumed by other creatures.

The key particle (dark yellow pixels), when eat, replicates the creature - creating an identical offspring, with change of random mutation - in place. The new offspring will have a standard energy to start its life, and will have a random rotation of -90 or +90 degrees. This is the only way a creature might reproduce (by eating key particles).

Both food particles and key particles are created in the environment only when a creature dies (except, of course, at the start of simulation).

The simulation can have two behaviours regarding the limits of the world:

• wrapping - in this case, a creature, when reaching the border, will reappear in the other end an continue moving. When both vertical and horizontal wrapping are enabled, the world will have a torus topology.
• collision - in this case, a creature, when reaching the border, will mirror horizontally (if reaching the width limit) or vertically (if reaching the heigth limit), therefore, changing its movement direction like a reflection.

Creature behaviour is governed by its structure. A creature structure can be represented by a set of connected dots (called cells, green pixels). One of this cells is a special one, and its called "head cell", colored yellow.

The head cell functions exactly as the other cells, so, it does not matter which cell is the head. The only difference is that, upon death, all regular cells are transformed into food particles, whist the head cell is transformed into a key particle.

The creature structure must obey certain rules, they are:

• All cells must be connected to the head.
• There must not exists cycles (i.e. starting from the head, and following neighbours, one cannot reach the same cell again).

By neighbours we mean only orthogonal, not diagonals.

With these rules in mind, lets see some concrete valid and invalid examples (in these examples, empty space is represented as ., and cells are represented as o).

These are all valid examples:

..... ..... .....
.o.o. .oo.. .o...
.ooo. .o.o. .ooo.
..... .ooo. .o...
..... ..... .....

On the other hand, the following examples are invalid, because they contain cycles:

..... ..... .....
.o.o. .ooo. .ooo.
.ooo. .o.o. .o.o.
.oo.. .ooo. .ooo.
..... ..... .....

At each reproduction (i.e. key particle eating) the offspring will be an exact copy of its parent, with a change of random mutation. A mutation is either adding or removing a single cell in a way that does not yield an invalid structure - therefore, an invalid structure can never occur.

Creatures moves in the environment depending on its structure. The movement depends solely on what is called "flagellum". These are cells that have only one neighbour. The flagellum, though, can have one of four possible configurations depending where the neighbour is: upward, downward, left, or right.

For example, the following structure has three flagellum, one faced upwards, one faced left, and the other faced right:

.....
..o..
.ooo.
.....

These flagella can be interpreted as direction pointers.

Each flagellum adds to a direction coefficient. In this example, the two horizontal flagellum (left and right) rule out each other, thereby resulting in a horizontal coefficient of zero. The upward flagellum adds a unbalanced vertical coefficient (in this case, -1).

So, by summing up the flagella directions, we came out with horizontal and vertical coefficients. To sum up, we must consider that upward flagella adds -1 to the vertical coefficient, downwards flagella adds 1 to the vertical coefficient; left flagella adds -1 to the horizontal coefficient, and right flagella adds 1 to horizontal coefficient.

The following examples have (0,-2), (1,-1), and (1, 0) of (horizontal, vertical) coefficients respectively:

..... ..... .....
.o.o. .oo.. .o...
.ooo. .o.o. .ooo.
..... .ooo. .o...
..... ..... .....

At each cycle, a creature may walk only one pixel in each direction. The actual move is draw from a creature's internal cyclic movement (i.e. it repeats), that have the following rule:

• A creature always stands still one cycle (i.e. walk (0,0))
• Then, at each i-th cycle, the creature will have a movement equals to (sign(H) if i < |H| else 0, sign(V) if i < |V| else 0), for i from 1 to max(|H|, |V|); Where H is the horizontal coefficient; V is the vertical coefficient; sign(x) is -1 if x < 0, 0 if x = 0, or 1 otherwise; and |x| is the absolute value of x.

For example, for a (horizontal, vertical) coefficient of (-1,2), a creature will have the following movement cycle:

• (0, 0)
• (-1, 1)
• (0, 1)

For coefficients equals to (1,1), we'll have the following cycle:

• (0, 0)
• (1, 1)

Likewise, for coefficients equals to (1,-1), we'll have the following cycle:

• (0, 0)
• (1,-1)

For coefficients equals to (0,10), we'll have the following cycle:

• (0, 0)
• (0, 1)
• (0, 1)
• (0, 1)
• (0, 1)
• (0, 1)
• (0, 1)
• (0, 1)
• (0, 1)
• (0, 1)
• (0, 1)

Note that, the bigger the coefficient, the faster will be the movement of the creature in that dimension, because it'll less often stand still. Also, for a creature to have perfect diagonal movement, it must have equal absolute values of the horizontal and vertical coefficients. Finally, creatures that have the coefficients equals to (0,0) will never move (that's a bad thing, because it won't eat and reproduce - leading quickly to death).

The structure of the creature also determines where are its "mouths". A creature might have zero or more mouths. Mouth is a place in an neighbour empty space where the creature can consume both food and key particles.

For a mouth to exist, the empty space should have at least three cell neighbours (orthogonal neighbours might have at most four cell neighbours; therefore it must have 3 or 4 neighbours). It doesn't matter if the cell is a regular (green) or head (yellow) type.

For example, in the following structures, we denote with an * the place where a mouth exists:

..... ..... ..... .......
.o*o. .oo.. .o... .o*o*o.
.ooo. .o*o. .ooo. .ooooo.
..... .ooo. .o... ..o*o..
..... ..... ..... .......

A creature with zero mouths (third example in the previous row) will obviously die pretty soon because it cannot feed itself, and, because it cannot eat key particles, will never reproduce. On the other hand, creatures with more mouths than the average will have selective advantage because they'll more easily be able to feed and reproduce.

The starting ancestral are creatures with the following structure:

.....
.o.o.
.ooo.
.....

They have one mouth and moving coefficients (0,-2), therefore, they move vertically down two of three of its movement cycle:

• (0, 0)
• (0, -1)
• (0, -1)

All the rotations of the ancestral also exists, so the movements are variate, but all of them orthogonal and the same speed.

Just to make clear the rotation and mirroring concepts. The following creatures are all equivalent (i.e. the same) (rotations and mirrors of the same structure):

...... ...... ..... ..... ..... ..... ...... ......
.o.oo. .oo.o. .oo.. ..oo. ..o.. ...o. ..ooo. .ooo..
.ooo.. ..ooo. .o... ...o. ..oo. ..oo. .oo.o. .o.oo.
...... ...... .oo.. ..oo. ...o. ..o.. ...... ......
...... ...... ..o.. ..o.. ..oo. ..oo. ...... ......
...... ...... ..... ..... ..... ..... ...... ......

The environment is started with some of them, and some amount of free food and key particles scattered around the world.

Pretty soon, we observe that the descendants will show a tendency to increase complexity of its structure by incorporating more mouths and better movements strategies (i.e. faster and diagonals).