1. INTRODUCTION
This is the documentation for Sand - a sandpile simulation,
programmed in Borland Delphi 2.0. This document describes how
the program works, and which parameters the simulation uses. See
the file theory.doc if you want some theoretical background on
sandpile models.
You use the program at your own risk. The program is not 100%
stable, though I've done my best to make it safe. To increase speed
I've disabled range checking in the program.
The source code has been included as freeware. Do with it whatever
you like. You don't have to credit me if you publish your changes,
but it would be a nice gesture.
2. CONCEPT
The simulation illustrates the principles of how a (much simplified)
sandpile behaves, when grains are added to it. The grains that are
added cause the sandpile to grow higher, but it may also cause grains
to fall down the sides of the pile, causing more grains to fall down,
etc. etc. Even though grains are added in random locations, the pile
will eventually become almost symmetric (it will become cone-
shaped).
The simulation was originally created to illustrate some underlying
principles of why the sandpile behaves like it does (how do ava-
lanches increase in size as the pile grows; how does the calculation
time increase; and the like).
The sandpile model used in the simulation doesn't have much to do
with a real sandpile (the model is quite flat, and grains can fall
uphill). However, you might like the patterns that the simulation
produces as it runs (watch out you don't get hypnotized ;). Also, the
model is an example of a certain kind of models, simply known as sandpile
models (see file theory.doc for more details).
3. HOW THE PROGRAM WORKS
You see the sandpile from the top. The height in each point on the
pile is between 0 and 8. If the height exceeds 4 the point topples,
which means that one grain moves to each of the neighbor points to
the north, south, east, and west. When one point topples, it may
cause one or more neighbors to topple too, causing an avalanche you
can follow on the screen.
You can specify which colors will represent the different heights
(click on the colored rectangles in the color dialog box). As you will
not be able to spot points of height > 4 because they topple
immediately, these colors are left out. The "trace" color is used when
you trace (with the trace function you can follow how the grains
move in the pile).
The sandpile has three parameters:
Surface: the maximum size of the sandpile (can be up to 255).
Add inside: the diameter in the center of the pile in which to add
grains (cannot exceed the pile size).
Rounds: the maximum number of rounds you want the simulation
to run (the same as: the maximum number of grains to add).
During the simulation you can see some statistics of the pile:
Added: tells how many grains are added (number of rounds).
Lost: grains that slide off the surface which the pile is placed
on.
Toppled: points that have toppled because they contained more
than 4 grains.
You can load and save piles. Some files have been included with the
program as examples.
Important: Note that drawing the sandpile is very time-consuming
(extremely so, if you ask me). Closing the window that shows the pile
will speed up calculations considerably, especially as the avalanches
get bigger.
Finally, a word of caution: for some reason I don't know, except it
probably has something to do with thread synchronization, the
program may crash if you press one of the buttons while the
simulation is running, and the window showing the pile is closed. I
advice you to stop/pause the simulation or make this window visible
before you load, save, exit, or change colors (these buttons seem to
give the most trouble). If you have any idea of the reason for this
problem, I'd be very happy to hear from you!
However, I've never personally experienced conflicts or other
problems between the program and other applications. I assume it's
safe to run the simulation in the background, while you do other
things. You might want to turn off your screen saver, though, as it
could steal the resources from the simulation when it's active.
Enjoy! (By the way, don't strain yourself looking for subliminal
messages in the sand. There aren't any ;)
Troels Jakobsen
tjak@get2net.dk
