Diffusion Limited Aggregation (DLA) Fractal

This fractal simulates a diffusive growth process similar to that often found in nature. It is generated by single points that randomly drift around until they find something to stick to. The title on this page was generated using this technique.

Diffusion Limited Aggregation (DLA) FractalMathematica 4.2, 8/12/04; C++ version: 2/10/05

(* runtime: 1 minute *)
n = 100; ix = iy = n/2; i = 0; SeedRandom[0]; image = Table[0, {n}, {n}];
Do[{ix, iy} = Floor[n(0.5 + 0.1{Cos[theta], Sin[theta]})] + 1; image[[ix, iy]] =1, {theta, 0, 2 Pi, Pi/180}];
While[(ix - n/2)^2 + (iy - n/2)^2 < (n/2)^2, theta = 2 Pi Random[]; {ix, iy} =Floor[n(1 + {Cos[theta], Sin[theta]})/2]; drift =True; While[drift, {ix, iy} = Mod[{ix + Random[Integer, {-1, 1}], iy + Random[Integer, {-1, 1}]}, n]; drift = Plus @@ Flatten[image[[Mod[ix + {-1, 0, 1}, n] + 1, Mod[iy + {-1, 0, 1}, n] + 1]]] == 0]; image[[ix + 1, iy + 1]] = 1 - i/n^1.5; i++];
ListDensityPlot[image, Mesh -> False, Frame -> False];



4 Responses to “Diffusion Limited Aggregation (DLA) Fractal”

  1. April 18, 2008 at 1:27 am

    I appreciate your work with fractals. I am working on a molecule, which I have named the genesis molecule because I believe that is is the scaffold of life. The mimimum size unit capable of self-assembly is a simple carbohydrate with a well defined repeat unit. However, the geometry and molecular contours of this structure appears to be suitable for an incubator for macromolecular synthesis, stem cell genesis, and organogenesis. The diffusion of a mixture of the polymer fragments during dehydration from aqueous salt solutions follows the DLA model. However, how do I add in the fact that the processs is molecular weight dependent? The polymer is a mixture of different sizes. How does the MW distribution and the polydispersity of the mixture affect the DLA model? May I use your purple image on my site? I will link to you. Thanks in advance.


  2. 2 nylander
    April 18, 2008 at 4:24 am

    Thank you Ray. Yes, you may use my image as long as you provide credit and a link to my site at http://bugman123.com

  3. 3 Frank
    July 16, 2009 at 8:41 am

    Your simulation is wonderful. Congratulations!
    My child learn how to simulate 3D diffusion limited aggregations with Matlab.
    Can You suggest how he must be done?
    Thank You in advance.


  4. December 6, 2014 at 4:47 am

    Awesome! II recently wrote a pen exploring cellular automata on a hex grid – the first result I got were snowflakes: http://codepen.io/sschepis/pen/yqheo

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