In this simulation, you can reproduce the relational drama of the lizards. We start from blue, orange and yellow
territories in the form of the sqaures of a chessboard, where male lizards compete with their neighbours.
At this chessboard, the opposite edges are again linked with each other. At the beginning, all fields are occupied randomly. Then, sequentially for each field, one of the four directly neighbouring fields is selected at random. If this selected field is the territory of the dominant rival, the considered field has to adopt its colour. In all other cases, it remains unchanged.
In the ong rectangle below the board, the relative number of fields in each colour, the population, is displayed. The lizards with the orange blotches depicted on the top replace the blue ones shown in the middel, those replace the yellow ones at the bottom. The yellow lizards, on their part, dominate the orange ones.
You can simplify the graphics by clicking on the checkbox "with compactation". In this case, there is a check after each move if there are fields with three or four neighbours of the same colour. If this is the case, this "minority" field has to adopt this predominant colour, too.
This also works on a hexagonal pattern, structured like a honeycomb. Actually, this is nicer than the squares,
but it is more difficult to program.
I have tried to explain here (in German) how I have done it and why the shape of the board looks so strange.
In his simulation, there are five colours trying to replace each other. The pecking order is in the sense as
in the population panel, top-down. (red replaces blue, blue replaces yellow ... and green replaces red).
There are two rule variations to click on :
(a) "Each colour replaces the following colour and the next but one", so red replaces blue and yellow etc.
(b) "Each colour replaces the following colour and the next but three", so red replaces blue and purple and so on.
A further feature is the button "a colour vanishes". If this is clicked on, one colour is deleted and statistically replacd by the four others.
Finally, there is also the button "a rectangle appears". With the slider thereunder, the size of this rectangle can be chosen before. Clicking on this button makes appear a rectangle of a random colour replacing all the other colours on the involved fields.
In this simulation, the replacement of a colour by another is linked to conditions. The option
"no constraints" means the choice of the same conditions as in the "Lizard" model here above.
The constraints on the upper half of the switch panel only refer to the case that a red field is to be replaced by a yellow one. The first condition says that this can only happen if at least one of the residual three neighbouring fields (the fourth is the aggressor) is also red.
The condition beside represents exactly the contrary : The red field can only be dyed yellow if there is no red neighbour.
In the second line, the condition can be set that red will only be replaced by yellow, if a least one - or if none - of the neighbouring fields is blue. Please note that blue is not directly involved in the act of red being replaced by yellow, thus somehow "neutral".
In the third line, the replacement of red by yellow can only take place if red has - respectively has not - one more yellow neighbour.
The constrains in the lower half of the switching panel are of the same kind as above, but for all colours at the same time. The constraints are now refering to the condition if the attacked has a neighbour/ has no neighbour of his own colour, of the colour of the attacker or of the neutral third colour.
By the way, te strange "crystallisation" visible on the screenshot can occur if there first are "no constraints" and then you click on the shown condition.
In this simulation, the same lizard subject is developed with balls, bouncing together like on a billards table.
Also here, the rules of "rock, paper, scissors" are applied. If a yellow ball hits a red one, the red ball will change its colour to yellow. If a red and a blue ball collide, the blue ball turns red. At the collision of a blue and a yellow ball, the blue one wins. Thus, for each colour there is one against which it wins and one other against which it loses.
In this simulation, the number of participants is again five. You can chose between two kinds of constraints :
With the top left condition, each colour can replace one other colour. Yellow replaces red, red replaces blue, blue replaces green, green replaces purple, and finally, purple replaces yellow. The circle is completed.
The condition top right discribes the opposite case - red replaces yellow etc.
Selecting the constraint at the bottom left, each colour get two opponets against which it wins and two against which it loses. With the constraints at the bottom right, again only the direction of the arrows has been inversed.
With the constraints in the lower half, we come back to the logics of "rock, paper, scissors", but with five symbols; each of them has two rivals against which it wins and two by which it is beaten.
I have learnt about a five-symbol version called "rock, paper, scissors, lizard (!), Spock". Before having known it, I had invented myself a more "classical" five symbol version expanded by "well" (forming a cycle with the hand) and "fire" (fingers up) : Well beats rock (falls in) and fire (extinguished) and loses against paper (covered) and scissors (swings open not falling in). The fire wins against paper (burns it) and scissors (forges it), and loses against rock (doesn't burn) and well.