This website features a collection of images generated using the rotor-router algorithm with various additional rules and constraints, as well as a 3D version of the algorithm that produces unique and fascinating patterns.

The rotor-router algorithm involves repeatedly sending a small chip from a source point, which moves according to a set of rules as it passes through each pixel. The chip stops at a pixel that has not previously encountered a chip, and initializes a rule for future chips to follow. This rule involves creating an arrow on the pixel that points in a specific direction, such as north. The chip then ends its journey and a new chip is sent from the source point to begin its own trip.

When a chip arrives at a pixel with an existing arrow, the arrow is moved and the chip follows the previous direction of the arrow. The sequence of arrow movements, such as "up, down, left, right," is repeated indefinitely.

The original rotor-router algorithm was described by J. Propp, and extensions to the algorithm have been developed in this site. You can find more information about the algorithm in the following link:

http://www.stat.berkeley.edu/~peres/router/router.html"

The rotor-router algorithm is known for producing strange and beautiful patterns, but it has a number of practical applications as well. One use of the algorithm is in solving mazes: by marking an arrow at each crossing with a stone or other marker, you can create a path through the maze that is Eulerian and visits all points.

Another interesting property of the rotor-router algorithm is that the order in which multiple chips are sent is not important, as all chips are identical. This makes the algorithm useful for tasks such as diffusion limited aggregation (DLA) and generating pseudo-random numbers. There is also a smart way to produce rotor-router pictures after a large number of iterations without running the chips one by one, discovered by L. Levine.

In addition to these applications, the rotor-router algorithm has been used to remove internal Moiré patterns that often occur with aggregation algorithms, and to produce interesting visual effects when applied to grids with initial values set as circles or squares. Some of these effects resemble magnetic dipoles.

Overall, the rotor-router algorithm is a versatile tool with a range of practical applications and the ability to generate unique and interesting patterns.

The Young experiment, also known as the double-slit experiment, is a classic physics experiment that demonstrates the wave-like properties of matter and light. In this experiment, a beam of particles is shone through a barrier with two slits, and the pattern that is observed on a screen behind the barrier shows interference fringes.

On this website, you may find attempts to create interferences in a similar manner using the rotor-router algorithm. In these experiments, chips from the rotor-router algorithm go through both slits and act as two diffusion centers. These slits behave like the slits in the Young experiment, and the pattern observed on the screen behind the barrier shows interference fringes similar to those seen in the classic experiment.

To see examples of these experiments, you can visit the 'interference with UDLR?' page on this website. The rotor-router algorithm provides a unique and interesting way to demonstrate the wave-like properties of matter and light and to observe the phenomenon of interference. Dual slit interferences with Rotor-router

One of the experiments on this website is dedicated to a 3D version of the rotor-router algorithm, which allows for the exploration of patterns in three dimensions. This experiment, called '3D rotor router - rotor router in z3,' offers the unique ability to view both the surface of a sphere and cut views in 3D.

The 3D rotor-router algorithm provides a fascinating way to visualize and investigate patterns in three dimensions, and the ability to observe the surface of a sphere and cut views adds an extra level of complexity and interest. In the future, it is hoped that there will also be an opportunity to use stereographic projection to further enhance the visualization of these patterns. 3d rotor-router

A interesting discovery shared on this website is that when an absorbing pixel is added to the plane of the rotor-router algorithm, the pattern that emerges at the absorbing point is similar to the pattern at the source. This finding adds an additional layer of complexity and interest to the rotor-router algorithm, and suggests that the patterns produced by the algorithm may have some underlying symmetry or structure. RotorRouter symetries with an absorbing pixel

The rotor-router algorithm, which uses the sequence "UDLR" to move chips through a grid, can reveal the pattern of a magnetic quadrupole or dipole moment when launched on a background initialized with alternating circles in two directions. You can see this effect for yourself by visiting the 'URDL version' page on this website.

While the patterns produced by the rotor-router algorithm may appear to be random noise, they are actually the result of a deterministic process that can be used to simulate the random diffusion aggregation process.

One modification to the algorithm that has been experimented with on this website is the initialization of empty cells reached by a chip. Instead of initializing these cells to a default value like "up," the current value at the source on the last chip launch is used. It is believed, although further proof is needed, that this modification improves the ability of the algorithm to simulate a random diffusion aggregation process.

Overall, the rotor-router algorithm is a versatile and interesting tool that can be used to study a variety of phenomena and produce a wide range of patterns and visual effects.

All images presented in this website are courtesy of Cedric Vandenweghe at https://sites.google.com/site/projectsced/home

Please feel free to leave me a comment at rotorrouterprojectsced (at) gmail.com.

content improved thanks to ChatGPT