Diffusion-limited aggregation: Difference between revisions
Spikeylegs (talk | contribs) DLA is method of modelling, changed wording and add modern example of electro-disposition with another figure Tags: Reverted Visual edit |
Spikeylegs (talk | contribs) m →Brownian tree: Modified wording Tags: Reverted Visual edit |
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At the time of their popularity (helped by a ''[[Scientific American]]'' article in the Computer Recreations section, December 1988), a common computer took hours, and even days, to generate a small tree. Today's computers can generate trees with tens of thousands of particles in minutes or seconds. |
At the time of their popularity (helped by a ''[[Scientific American]]'' article in the Computer Recreations section, December 1988), a common computer took hours, and even days, to generate a small tree. Today's computers can generate trees with tens of thousands of particles in minutes or seconds. |
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Diffusion-limited Electrodeposition can be accurately modelled using |
Diffusion-limited Electrodeposition can be accurately modelled using a computer simulated DLA(utilizing [[Fick's laws of diffusion]] as it's moving algorithm)<ref>{{Cite journal|last=Lupo|first=C.|last2=Schlettwein|first2=D.|date=2018-11-30|title=Modeling of Dendrite Formation as a Consequence of Diffusion-Limited Electrodeposition|url=http://dx.doi.org/10.1149/2.0231901jes|journal=Journal of The Electrochemical Society|volume=166|issue=1|pages=D3182–D3189|doi=10.1149/2.0231901jes|issn=0013-4651}}</ref> |
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[[File:DLA step 1thru10.png|thumb|288x288px|Example showing first 10 steps of DLA, at each step a random walk steps towards the cluster(light grey) and "sticks" becoming the cluster(black)<ref>{{Cite web|title=Note (a) for The Phenomenon of Continuity: A New Kind of Science {{!}} Online by Stephen Wolfram [Page 979]|url=https://www.wolframscience.com/nks/notes-7-6--diffusion-limited-aggregation-dla/|access-date=2021-03-01|website=www.wolframscience.com|language=en}}</ref>]] |
[[File:DLA step 1thru10.png|thumb|288x288px|Example showing first 10 steps of DLA, at each step a random walk steps towards the cluster(light grey) and "sticks" becoming the cluster(black)<ref>{{Cite web|title=Note (a) for The Phenomenon of Continuity: A New Kind of Science {{!}} Online by Stephen Wolfram [Page 979]|url=https://www.wolframscience.com/nks/notes-7-6--diffusion-limited-aggregation-dla/|access-date=2021-03-01|website=www.wolframscience.com|language=en}}</ref>]] |
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Revision as of 21:52, 1 March 2021
Diffusion-limited aggregation (DLA) is the process whereby particles undergoing a
The clusters formed in DLA processes are referred to as
Computer simulation of DLA is one of the primary means of studying this model. Several methods are available to accomplish this. Simulations can be done on a lattice of any desired geometry of embedding dimension (this has been done in up to 8 dimensions)[2] or the simulation can be done more along the lines of a standard molecular dynamics simulation where a particle is allowed to freely random walk until it gets within a certain critical range whereupon it is pulled onto the cluster. Of critical importance is that the number of particles undergoing Brownian motion in the system is kept very low so that only the diffusive nature of the system is present.
Brownian tree
A Brownian tree, whose name is derived from
A Brownian tree is built with these steps: first, a "seed" is placed somewhere on the screen. Then, a particle is placed in a random position of the screen, and moved randomly until it bumps against the seed. The particle is left there, and another particle is placed in a random position and moved until it bumps against the seed or any previous particle, and so on.
Factors
The resulting tree can have many different shapes, depending on principally three factors:
- the seed position
- the initial particle position (anywhere on the screen, from a circle surrounding the seed, from the top of the screen, etc.)
- the moving algorithm (usually random, but for example a particle can be deleted if it goes too far from the seed, etc.)
Particle color can change between iterations, giving interesting effects.
At the time of their popularity (helped by a Scientific American article in the Computer Recreations section, December 1988), a common computer took hours, and even days, to generate a small tree. Today's computers can generate trees with tens of thousands of particles in minutes or seconds.
Diffusion-limited Electrodeposition can be accurately modelled using a computer simulated DLA(utilizing Fick's laws of diffusion as it's moving algorithm)[3]
Artwork based on diffusion-limited aggregation
The intricate and organic forms that can be generated with diffusion-limited aggregation algorithms have been explored by artists. Simutils, part of the
See also
References
- .
- .
- ISSN 0013-4651.
- ^ "Note (a) for The Phenomenon of Continuity: A New Kind of Science | Online by Stephen Wolfram [Page 979]". www.wolframscience.com. Retrieved 2021-03-01.
- ^ Hickman, Bert (2006). "What are Lichtenberg figures, and how do we make them?". CapturedLightning.com. Retrieved June 6, 2019. Last updated: 03/26/19. Created: 02/11/06 or earlier at http://lichdesc.teslamania.com.
- ^ a b Schmidt, K. (February 20, 2010). "simutils-0001: Diffusion-limited aggregation". toxiclibs.org. Retrieved June 6, 2019.
External links
- Media related to Diffusion-limited aggregation at Wikimedia Commons
- JavaScript based DLA
- Diffusion-Limited Aggregation: A Model for Pattern Formation
- A Java applet demonstration of DLA from Hong Kong University
- Free, open source program for generating DLAs using freely available ImageJ software
- TheDLA, iOS app for generating DLA pattern
- Open-source application in C for fast generation of DLA structures in 2,3,4 and higher dimensions