A Brownian tree example

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. Download high resolution version (855x731, 33 KB)Image of a brownian tree with the following characteristics: seed in bottom of the screen. ... Download high resolution version (855x731, 33 KB)Image of a brownian tree with the following characteristics: seed in bottom of the screen. ... Robert Brown (December 21, 1773 - June 10, 1858) is acknowledged as the leading British botanist to collect in Australia during the first half of the 19th century. ... An example of 1000 simulated steps of Brownian motion in two dimensions. ... // Events and trends The 1990s are generally classified as having moved slightly away from the more conservative 1980s, but otherwise retaining the same mindset. ... An example of 1000 simulated steps of Brownian motion in two dimensions. ... A crystal dendrite is a crystal that develops with a typical multi-branching tree-like form. ...

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.

A circular Brownian tree

The resulting tree can have many different shapes, depending on principally three factors: Image of a brownian tree with the following characteristics: seed in the center particles starting from an outer circle color randomly changed at each iteration generated with a home-made program and released under the GFDL. Original version (800x600 pixels) File links The following pages link to this file: Brownian... Image of a brownian tree with the following characteristics: seed in the center particles starting from an outer circle color randomly changed at each iteration generated with a home-made program and released under the GFDL. Original version (800x600 pixels) File links The following pages link to this file: Brownian...

• 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. Scientific American is one of the oldest and most serious popular-science magazines. ... 2003 is a common year starting on Wednesday of the Gregorian calendar. ...

External link

• Five Cellular Automata Windows software for exploring five different cellular automata, including Brownian trees (see 'Diffusion-Limited Aggregation')