This repo contains a series of visual experiments built with JavaScript that explore the topic of diffusion-limited aggregation (DLA) as a method for generating interesting 2D forms.

I am particularly interested in the application of such techniques in the context of digital fabrication, so these experiments will be more focused on schematic representations (colorless, vector-based, SVG/STL exports) over purely visual effects.

About diffusion-limited aggregation

Diffusion-limited aggregation (DLA) is a process in which randomly-moving particles diffuse through a medium and clump together (aggregate) over time to form long, fractal, branch-like chains (sometimes called Brownian trees). It closely models various interesting phenomena seen in nature at different scales and in different mediums.

A classic example is that of the formation of copper sulfate crystals in the presence of an electrodeposition cell. When electricity is applied, individual copper atoms are stripped from the system's anode and randomly float (diffuse) through the liquid medium until they come in contact with other copper atoms that have accumulated on the system's cathode where they form a strong molecular bond and aggregate over time.

Another example can be seen in the rather more violent phenomena of Lichtenberg figures, wherein an electrical discharge of very high voltage travels through an insulator like wood, burning a curious fractal branching structure in it's wake. In this example, it would seem that the electrical discharge itself diffuses through the wood, limited by the insulating nature of the wood, forming an "aggregate" of burnt wood as it progresses.

A note on lattices and parameterization

In classical implementations this algorithm acts upon a regular 2D grid of pixels wherein each "particle" can have up to 8 neighbors. Though simplistic, this so-called "on-lattice" approach can run at blistering speeds because no expensive distance calculations, spatial indexing, or collision detection is required - just array lookups.

However, this approach results in an inherently low fidelity raster image that has a pretty characteristic aesthetic style and limited usefulness in modern digital fabrication workflows. In the world of digital fabrication vector-based graphics are preferred because they can be easily transformed into machine toolpaths and manipulated in interesting ways in CAD software.

To achieve vector-based results from the DLA process one must move away from pixels and towards particles, which also affords one the ability for more parameterization that can be fun to explore creatively. For example, one could vary the size, shape, and movement behaviors of these particles to achieve interesting effects.

Keyboard commands

Key	Result
w	Toggle visibility of walkers
c	Toggle visibility of clustered particles
s	Toggle visibility of custom SVG shapes
r	Restart simulation
f	Toggle frame
l	Toggle line rendering effect
e	Export and initiate download of current drawing as SVG file
t	Toggle visibility of helpful text
Space	Pause/unpause simulation

Parameters

Parameter	Value	Default	Description
CircleDiameter	Number	5	Default size of walkers, if none is provided through local Settings.
InitialClusterType	Point, Ring, Random, or Wall	Point	Default initial cluster pattern, if none is provided through local Settings.
ShowClusters	Boolean	true	Visibility of clustered particles on load.
ShowWalkers	Boolean	true	Visibility of walkers on load.
ShowShapes	Boolean	true	Visibility of custom SVG shapes on load.
MaxWalkers	Number	20000	Maximum number of walkers - lower numbers mean better performance, but fewer hits.
WalkerSource	Edges, Circle, Random, Random-Circle, or Center	Center	Where new walkers are spawned.
ReplenishWalkers	Boolean	false	Add new walkers whenever they become stuck to clusters.
BiasTowards	Top, Bottom, Left, Right, Edges, Center, Equator, or Meridian	Center	Direction to move all walkers each iteration.
BiasForce	Number	1	Magnitude of force to move walkers towards their bias direction.
UseFrame	Boolean	true	Constrain sketch to a box centered on the screen.
FrameSize	Number or [width, height]	900	Size of frame.
CaptureLines	Boolean	true	Enable building of an internal buffer of line segments between all connected particles. Can be disabled if it impacts performance at large scales.
RenderMode	Shapes or Lines	Shapes	Method of drawing particles. Can draw the shapes as they exist (Shapes), or only draw lines between connected particles (Lines).
UseColors	Boolean	false	Enable the use of colors defined by objects below.
UseStroke	Boolean	false	Draws all circles/polygons with a 1px stroke matching the background color.
BackgroundColor	Object with h, s, b properties		Color of canvas background in HSB format.
WalkerColor	Object with h, s, b properties		Color of walkers in HSB format.
ClusterColor	Object with h, s, b properties		Color of clustered particles in HSB format.
ShapeColor	Object with h, s, b properties		Color of custom SVG shapes in HSB format.
LineColor	Object with h, s, b properties		Color of lines when using Lines for RenderMode.
FrameColor	Object with h, s, b properties		Color of frame, if enabled with UseFrame.

Packages used

• p5.js for canvas drawing and miscellaneous helper functions (like lerp and map).
• Webpack for modern JS (ES6) syntax, code modularization, bundling, and serving locally.
• collisions for robust, lightweight collision detection without the use of a full physics package.
• svg-pathdata for parsing path information from SVG files in order to create custom shapes.
• svg-points for generating the d attribute of SVG <path> elements for export feature.
• file-saver for initiating a download of exported SVG fles to the user's machine.

Running locally

1. Run npm install in both the ./build and ./core folders.
2. Run npm run serve in the ./build folder to start a local development server and launch it in a browser.

To statically build the code in this repo, run npm run build in the ./build folder.

Going further

The code in this repo can be improved or optimized in a few ways to achieve faster performance and larger scales. Here are some ideas that come to mind:

1. Rather than using brute-force movement and collision detection (which limit overall scale + speed), implement an algorithm like Michael Fogleman's dlaf. This may mean that one would have to do away with variable particle shapes and sizes, but I imagine variable sizes could be accommodated with some tweaking.
2. Port code over to a more performant language / library like openFrameworks or Cinder.

References

• DLA - Diffusion Limited Aggregation by Paul Bourke
• Diffusion-limited aggregation on Wikipedia
• Coding Challenge #34: Diffusion-Limited Aggregation by Dan Shiffman (Github repo)
• Coding Challenge #127: Brownian Tree Snowflake by Dan Shiffman (Github repo)
• simutils-0001: Diffusion limited aggregation by Karsten Schmidt (toxiclibs)
• Diffusion Limited Aggregation (PDF) by André Offringa
• Simulate: Diffusion-Limited Aggregation from FORM+CODE book examples
• Diffusion-Limited Aggregation by Softology
• Diffusion-limited aggregation: A kinetic critical phenomenon? (PDF) by Leonard M. Sander
• Dendron Processing sketch by Golan Levin

Samples