
Rounder Router 
Illustrating a "quasirandom" model of diffusion by
Jim Propp. The applet demonstrates threestate and twostate versions of the same model.
In the threestate model,
if n particles are added to the top brick of the triangle, round(n/3) of them
go down to the left, and round(2n/3) go down to the right. Particles that go
left of the leftmost bricks are "absorbed". Others continue down the pile.
The number of particles that don't fall off the left after n are
added at the top call that f(n) approaches n/2. Strangely, f(n) >= n/2,
never less, until the first time at n = 5495 (see
wander6b.txt and
wandergraph.jpg).
If you look at where particles go when added incrementally, it depends
on how many particles have arrived at a brick previously, mod 3.
If that's zero, I color the brick
cyan, and the next particle goes right. One:
magenta, left. Two:
yellow, right.
In the twostate model, floor(n/2) particles go left and ceil(n/2) go right.
Click on the "flag" in the upper right to toggle between models.
Click anywhere else on the applet to pause or continue.
Makefile (4K) 
applet/ 
source code for the applet on the right 
sound/ 
source code for wav/aiff output (and input) 
wander.tgz (294K) 
sources of everything (+applet .jar),
but not wandergraph.jpg or generated files 
wander5 (2K) 
wander6 (3K) 
Python program to print recordbreakers and stats
for f(n)  n/2 
wander6b.txt (4K) 
table from wander6 (reformatted by hand) 
wander7.c (2K) 
Generate stream of 2^27 characters '=' if f(n)==f(n1),
'>' if f(n)==f(n1)+1. 
wander7out.gz (8556K) 
gzipped output of wander7 
wandergraph.jpg (142K) 
graph of max and min of f(n)n/2, and 'necessary
length of table' 
wandersweep.c (4K) 
Turn wander7out into audio, with sample rate sweeping
from 1000Hz to ~20MHz. 
wandersweep.mp3 (470K) 
the audio 
This page was made with a
php script.
Last change November 12, 2013.
Steve Witham
Up to my home page.
The Rounder trademark belongs to Rounder Records.

