Dendritic Shapes are multi-branches shapes that look like tree branches. They are also the same shapes of lightings, corals, and even neurons! In this paper, the literature on generating dendritic shapes is discussed as well as an introduction of a new algorithm.
Ling Xu, David Mould
We present a method for creating geometric models of dendritic forms. Dendritic shapes are commonplace in the natural world; some examples of objects exhibiting dendritic shape include lichens, coral, trees, lightning, rivers, crystals, and venation patterns. Our method first generates a regular lattice with randomly weighted edges, then finds least-cost paths through the lattice. Multiple paths from a single starting location (or generator) are connected into a single dendritic shape. Alternatively, path costs can be used to segment volumes into irregular shapes. The pathfinding process is inexpensive, and admits control handles including endpoint placement, distribution of generators, and arrangement of nodes in the graph.
I really liked the writing style of this paper. It introduces the basic concepts and previous literature on dendritic shapes with a follow-up explanation of the famous methods such as L-systems and DLA. Then, it introduces a new algorithm based on path planning.
In this algorithm, the graph edges are populated with random costs, and then some nodes are chosen to be generators. Moreover, endpoints are placed on the graph and using a greedy breadth-first search, a path is drawn from the endpoints to the closest generator.
Using a refinement process that iterates on the previously created paths, the dendritic shapes end up being less rigid or Manhattan-like.
The main application of the algorithm was to create a 2D dendritic shape, but since it is easily extendable to the third dimension, and with the freedom of using your own textures and geometric shapes, you can use the algorithm to create stunning objects such as deep-sea corals.
The paper can be accessed at: http://people.scs.carleton.ca/~mould/papers/den.pdf