manual.txt

模拟2维沙堆效果

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
[e-mail]