Brownian tree

Brownian tree

A Brownian tree, whose name is derived from Robert Brown via Brownian motion, is a form of computer art that was briefly popular in the 1990s, when home computers started to have sufficient power to simulate Brownian motion. Brownian trees are mathematical models of dendritic structures associated with the physical process known as diffusion-limited aggregation.

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, and so on.

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 Amateur Scientist section), a common computer took hours, and even days, to generate a small tree. Today's (2003) computers can generate trees with tens of thousands of particles in a few minutes.

These trees can also be grown easily in an electrodeposition cell, and are the direct result of diffusion-limited aggregation.


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Brownian motion — This article is about the physical phenomenon; for the stochastic process, see Wiener process. For the sports team, see Brownian Motion (Ultimate). For the mobility model, see Random walk. Brownian motion (named after the botanist Robert Brown)… …   Wikipedia

  • List of mathematics articles (B) — NOTOC B B spline B* algebra B* search algorithm B,C,K,W system BA model Ba space Babuška Lax Milgram theorem Baby Monster group Baby step giant step Babylonian mathematics Babylonian numerals Bach tensor Bach s algorithm Bachmann–Howard ordinal… …   Wikipedia

  • Fractal — A fractal is generally a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced size copy of the whole, [cite book last = Mandelbrot first = B.B. title = The Fractal Geometry of… …   Wikipedia

  • Diffusion-limited aggregation — A DLA cluster grown from a copper sulfate solution in an electrodeposition cell Diffusion limited aggregation (DLA) is the process whereby particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such… …   Wikipedia

  • Dendrite (crystal) — Manganese dendrites on a limestone bedding plane from Solnhofen, Germany. Scale in mm. A crystal dendrite is a crystal that develops with a typical multi branching tree like form. Dendritic crystal growth is very common and illustrated by… …   Wikipedia

  • Loop-erased random walk — In mathematics, loop erased random walk is a model for a random simple path with important applications in combinatorics and, in physics, quantum field theory. It is intimately connected to the uniform spanning tree, a model for a random tree.… …   Wikipedia

  • garden and landscape design — Introduction       the development and decorative planting of gardens, yards, grounds, parks, and other types of areas. Gardening and landscape design is used to enhance the settings for buildings and public areas and in recreational areas and… …   Universalium

  • Schramm–Loewner evolution — In probability theory, Schramm–Loewner evolution, also known as stochastic Loewner evolution or SLE, is a conformally invariant stochastic process. It is a family of random planar curves that are generated by solving Charles Loewner s… …   Wikipedia

  • Phylogenetic comparative methods — When applied to comparative data, conventional statistical methods assume, in effect, that all species are completely unrelated. As if they descended from a big bang of special creation. Such a scenario can be depicted as a star phylogeny (left) …   Wikipedia

  • Mathematical finance — is a field of applied mathematics, concerned with financial markets. The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory. Generally, mathematical finance will… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”