I first heard about Huegene after watching the following video from Dave Ackley.

Similarities to Wa-Tor

Huegene is similar to Wa-Tor with the following differences;

1. Plants and herbivores rather than fish and sharks.

2. Plants cannot move like fish can. They spread through self propagation.

3. Herbivores have a probability chance of eating plants based on how close in color the herbivores and plants are.

Color Genes

Both the plants and herbivores have genes that determine their color.

When a new plant or herbivore is created it has a slightly mutated color from the parent. This results in plants growing in clumps of similar colors.

Plant Consumption Probability

This is the main difference between Huegene and Wa-Tor. In Wa-Tor the sharks happily gobble up any fish they land on. In Huegene the herbivores have a probability of eating a plant based on how close in color they are to the plant. So a blue herbivore will have a greater chance of eating a light blue plant than a yellow plant.

Herbivores eat the plants around them with the most similar color, which leads to the less similar plants in the area being able to thrive which then have more resistance to the herbivores in the area. The herbivores also mutate and can adapt to eating the new plant colors. This feedback cycle continues as the plants and herbivores adapt to the changes in each other.

Gene Color Methods

For the gene colors I use the following 3 options;

1. Hue. Hue is a floating point value between 0 and 1. For display the HSL(hue,1.0,0.5) value is converted to RGB.

2. RGB. Each plant or herbivore has 3 color genes for red, green and blue.

3. Hue and Saturation. Hue is between 0 and 1. Saturation is between 0.5 and 1. For display the HSL(hue,saturation,1) value is converted to RGB.

The following three sections explain how these different gene methods are used to determine a probability of a herbivore eating a plant next to it.

Hue Genes

Hue is a floating point value between 0 and 1. It is converted to RGB values for display.

The following code is used to determine if a herbivore eats a plant near it.

//difference between hue values
//wraparound difference - make sure difference is between 0 and 0.5
if difference>0.5 then difference:=1-difference;
//scale difference to between 0 and 1
//test probability
if random*probabilityfactor<(1.0-difference) then EatPlant

The difference takes into account the fact that the Hue values wrap around from 1 back to 0 on the hue color wheel. For example, if you have a plant hue at 0.1 and a herbivore hue at 0.9 you want their difference to be calculated as 0.2 and not 0.8.

I also added a “probability factor” in. If this is greater than 1 it lessens the chance of the herbivore eating the plant. If you get a simulation that the herbivores are too plentiful increasing this factor will help keep them under control.

RGB Genes

Each plant and herbivore now has 3 red green and blue values that are used for display and the probability of the plants being eaten by herbivores.

//difference between RGB values
//test probability
if random*probabilityfactor<(1.0-difference) then EatPlant

Hue and Saturation

Now takes into account hue and saturation values. Hue is between 0 and 1. Saturation is between 0.5 and 1.

//difference between hue values
//wraparound difference - make sure difference is between 0 and 0.5
if difference>0.5 then difference:=1-difference;
//saturation contributes 50% of difference value
//test probability
if random*probabilityfactor<(1.0-difference) then EatPlant

Other Examples

Plants actively look for empty neighbor locations to spread into. Herbivores move at random rather than actively looking for plant neighbors.

Plants actively looking for empty neighbors. Herbivores hunting for available plant neighbors.

Plants spread randomly. Herbivores hunt for available plant neighbors.

Sample Movie


Huegene is now included in Visions of Chaos.



Wa-Tor is a simulation of fish vs sharks in a toroidal wraparound world. It was devised by AK Dewdney in 1984 and published in Scientific American under the name “Sharks and fish wage an ecological war on the toroidal planet Wa-Tor

The original Wa-Tor simulations took place on a VAX system with a display 80×23 characters in size. Each step of the simulation took a while to run (no exact time specs given). It is interesting to read in Dewdney’s article that to test a theory he had about the system he let a setup run overnight to see what happened in the morning. Now with a decent computer you can run these over thousands of cells in almost real time.


The world consists of a 2D array that wraps around at the edges. When you have the wrapped edges the world becomes a donut (or toroid) shape.

A number of sharks and fish are randomly distributed into the world.

Fish look for empty cells directly next to themselves (using a von Neumann neighborhood of neighbor cells directly north, south, east and west) and randomly move into one of them. If they are older than a specified breed age they will leave a child fish behind in their current location.

Sharks look for fish next to themselves and randomly eat one of them if found. When they move they will leave a child shark in their old spot if they are older than a specified breed age. If no fish are found they will randomly move into an available empty space. If they do not eat their starvation level increases. If they starve for too many steps of the simulation they die and are removed from the world.

Here is an example of Wa-Tor. Green pixels are fish, red pixels are feeding sharks, gray pixels are sharks.

If you balance the settings right this sort of simulation will continue to cycle indefinitely.

Wa-Tor Parameters

Wa-Tor is controlled by the following parameters the user can play with;

Fish breed age – how many simulation steps does a fish need to survive for before it can give birth to baby fish. For these simulations I used 3 cycles.

Shark breed age – how many simulation steps does a shark need to survive for before it can give birth to baby fish. 15 cycles.

Shark starve time – how many simulation steps it takes for a shark to starve to death if it does not eat. 10 cycles.

Random Movement

An alternative method is to allow fish and sharks to only move randomly.

Fish pick one of the 4 directions at random. If it is empty they move into it and potentially have a child. If it is occupied they do nothing.

Sharks also pick a random direction. If a fish is there the shark eats it. If the spot it empty the shark moves into it. If it is occupied the shark does nothing.

Here is an animated gif showing fish and sharks both moving randomly.

Color Fish

This was a quick idea I had. Each fish has a color assigned to it. When it has a child fish, the child fish has the same color with slightly different RGB values. This way you can see how a “family” of similar fish spreads.


That about covers all there is to say about Wa-Tor. It is a good project if you are starting to program or enjoy these sort of agent-based modelling systems.

Wa-Tor is available in Visions of Chaos.




This is a relatively simple simulation of multiple species fighting for survival.

Simulation World

A terrain is generated using Perlin noise. The noise values are blurred to smooth out the edges a little.


Multiple types of creatures are created that inhabit the world. They each have properties like;
X and Y position – where the creature is in the world
Radius – how large the creature is
Direction – what direction the creature is facing
Speed – how far the creature moves each step of the simulation
Color – what color it is so creature types can easily be distinguished from one another
Sides – creatures are shown as polygons with between 3 and 8 sides
Age – how many simulation steps has the creature lived for
Maximum Age – if a creature reaches this age it dies of old age
Minimum and Maximum Breed Ages – a range of ages that the creature can reproduce

The simulation is started by creating a bunch of random creatures in the world. They all move according to their properties.


When 2 creatures come into contact with each other they fight for survival. At this stage I have 3 possible fight methods to determine which creature wins;
1. Random – one of the creatures in the fight is randomly chosen to die
2. Attacker wins – whichever creature first moves and hits another creature kills the creature it hits
3. Strongest wins – Creature strength goes up from birth to middle age then down again as the creature ages. This is so “babies” and “elderly” creatures are not as strong in battle against middle age creatures.


Creatures have a chance to duplicate themselves if they are between a minimum and maximum breed age and if there is room near them for the child creature to be born into. There is an option for the child properties to be mutated slightly (or not so slightly).


Here is a sample movie showing a full run that lasts until one of the species manages to kill all others. No mutations in this example.

Species is now available as a mode within Visions of Chaos.


Primordial Particle Systems

Primordial Particle Systems

A while back I was playing with Particle Life simulations. At that time, another video I came across was the following

Click here to read the paper “How a life-like system emerges from a simple particle motion law” that describes how it works in great detail.

Primordial Particle Systems

For a simpler overview I recommend this page by Brian H that includes snippets of the source code that helped me get my version working.

Primordial Particle Systems

My even (hopefully) simpler explanation is as follows;

1. Fill the simulation space with a bunch of particles.
2. Particles have settings for radius, alpha, beta and velocity.
– radius is how far around itself each particle can sense the other particles.
– alpha is the fixed rotation amount. Each particle turns by this amount each step of the simulation.
– beta is the proportional rotation. This is the amount the particle turns depending on its neighbor particles.
– velocity is how far the particles move forward each step.
3. Each particle maintains a heading which is the direction it is facing.
4. Each of the particles move by the following steps
– Count how many neighbor particles are within the radius
– Work out how many of them are to the left and right of the particle
– Turn towards the left or right with the larger count
– Move forward

That’s all there is. From those relatively local and simple steps you can get some nice cell like and amoeba like structures emerging.

Primordial Particle Systems

More sample images in this gallery.

The following movie shows some example results created with the latest version of Visions of Chaos.


Physarum Simulations

Physarum Polycephalum

Physarum Polycephalum aka slime mold is made up of a vast number of individual single cell organisms. These organisms have no brains or intelligence, but complex behaviors emerge when many of them are put together. Depending on their environment they move like what seems to be a much more complex entity.

Here are some great videos about slime molds with some awesome time lapse footage.

Once you have watched those you should hopefully have a better appreciation for the simple slime mold and the rest of this post will make more sense.

Here is one final video showing time lapse footage of various Physarum

Simulating Slime Molds

I have been interested in trying to simulate slime molds fror years now and my interest was once again peaked from seeing Sage Jenson‘s Physarum page here describing his simulations.

Sage was inspired by the paper Characteristics of Pattern Formation and Evolution in Approximations of Physarum Transport Networks.

He gives this simple diagram explaining the steps.

The basic explanation is a bunch of particles move over an area turning towards spots with higher concentrations of a pheromone trail. They also leave a trail as they move. These basic steps create interesting patterns and structures.

My method

Physarum Simulation

Following the principals from Sage and the paper, this is how my take on simulating Physarum works.

Physarum Simulation

1. Create a 2D array that tracks the pheromone trail intensity at every pixel location. Initially all spots are set to 0 intensity. I tried setting various shapes and perlin noise clouds to start, but the moving particles quickly erase any starting shapes and create their own paths so I just start with an empty space. Sage’s examples show interesting patterns and structures when starting with circles or other shapes, so I need to do some more work on start patterns.

Physarum Simulation

2. Create a list of particles with properties heading (direction/angle the particle is moving), x,y (positions), sense angle (how wide the particle looks to the left and right) and sense distance (how far in front the particle looks), turn angle (how quick the particle turns towards the sensed areas). I set the number of particles to match the image width multiplied by the image height. That seems to nicely adjust the particle count when changing image sizes.

Physarum Simulation

3. Main loop

Physarum Simulation

a) Display. For display I scale the minimum and maximum trail values to between 0 and 255 for a gray scale intensity (or to be used as an index into a color palette, but simple gray scale seems to look the best).

Physarum Simulation

b) Each particle looks at the 3 locations in front of it based on the sense angle and distance. You then work out which of the left, front and right spots have the highest concentration of the pheromone trail.

Physarum Simulation

c) Turn the particle towards the highest pheromone intensity. ie if the left spot is highest then subtract turn angle from the particle heading. If the front is highest do not make any change to the particle heading. If the right is highest add turn angle to the particle heading. You can also reverse this process so the particles turn away from the highest pheromone levels.

Physarum Simulation

d) Move the particle forwards by a specified move amount.

Physarum Simulation

e) Deposit an amount of pheromone onto the trail to increase it.

Physarum Simulation

f) Blur the trail array. This simulates the pheromones diffusing over the surface. I use this quick blur with an option for a blur radius between 1 and 5.

Physarum Simulation

g) Evaporate the trail by a small amount. This slowly decays the amount of pheromone.

Physarum Simulation

Repeat the main loop as long as necessary.

Physarum Simulation


See my Physarum Simulations gallery for more images.

Here is a movie with some example results showing the simulations running. For the display the pheromone trail intensities are mapped to a gray scale palette (brighter = higher intensities).

Multiple Species Physarum Simulations

Physarum Simulation

My next idea was to have multiple Physarum types in the same area. For these cases I used 3 sets of Physarum (3 groups of particles with their own unique settings) as shown in the following settings dialog.

Physarum Simulation

Each of the pheromone trail intensities are then converted to RGB color components.

Physarum Simulation

This works but the results are just 3 separate simulations that do not interact. The idea is to have each of the particle types attract to their pheromones, but move away from the other 2 types of pheromones.

Physarum Simulation

The main change is in the pheromone detection and turn code. For the single Physarum simulation the particles look left, forward and right and then turn and move based on the location with the highest pheromone concentration. For 3 particle types they take into account their pheromone concentrations but subtract the pheromone concentrations of the other 2 types. For example if the 3 trail/pheromone arrays are called rtrail, gtrail and btrail, then the red particles pheromones are calculated by using rtrail[x,y]-gtrail[x,y]-btrail[x,y]. The highest concentration of left, forward and right is then turned and moved towards.

Physarum Simulation

More example images can be seen in my Physarum Simulations Gallery.

Here is a sample movie showing some of the multiple species results.

Physarum Image Processing

This was inspired after seeing the following video from Magic Jesus.

A bunch of Physarum particles start on the surface of an image. The particle colors are based on the image color they start on.

After this let them wander around the image area following Physarum simulation rules with a slight change. In this case rather than turning left or right based on a pheromone trail intensity, they turn towards the pixel that is closest in color to themselves.

This is my result after running Physarum simulations on three colorful paintings. The first and third are from Leonid Afremov and the second by Kandinsky (same painting as in Magic Jesus’ example movie).

These would look great on a large wall in a modern art gallery. Playing slowly enough so you could just notice the changing colors (like clouds moving slow enough you don’t notice they change until you look away and back again). The exhibits with those dark rooms you enter and read the little white plaque with a blurb on what it is all about. “The slow interplay of colors represents the human condition and the struggles of how humans still cannot find a peaceful equilibrium of coexistence with themselves and the planet.”


See the following movie for a more detailed explanation of this blog post and the Physarum modes within Visions of Chaos.


Both single and multiple species Physarum Simulations and Physarum Pixel Flow are now included with the latest version of Visions of Chaos.


Clusters and Particle Life

This is another great example of emergence. Complex behavior results from many individual particles following simple rules.

Jeffrey Ventrella explains his Clusters here.

Here is another particle based life model

I learned about Clusters when Code Parade posted the following video explaining his version of Clusters he calls Particle Life.

The source code to Particle Life was generously shared here so I had a go at converting the code and playing with these myself.


Here are some of my results.

Extension Into 3D

Once I had the 2D version working, extending into 3D was the next step. These movie parts use the same settings as in the 2D movie above.


Both the 2D and 3D Particle Life are now included with Visions of Chaos.