Download version 1.3 (macOS 11 Big Sur → 15 Sequoia)

Download version 1.2 (Mac OS X 10.0 → 10.12?)

---

The point / what this screen saver is doing:

Simple systems, with simple rules, can develop interesting phenomena. You can learn a lot about a system of equations by watching what macroscopic effects accrue when you let the system evolve.

The rules of this system are simple: Objects have a position, momentum and charge. They interact by an electric-like force between them: (The ~ sign means "proportional to")



When objects hit the wall, they bounce elastically (without losing energy). Actually, that's not quite true. If they go too fast, I make them slow down when they hit a wall. I do this because there is little in place currently to slow down objects except accidental dragging from other charges. As I update this, the simulation will become more realistic.

[2024 note: I never once noticed that I misspelled "distace" in the graphic of the formula above. Lesson: Always wait 20 years for a final edit pass.]

Current problems with the screen saver:

1. Proper elastic collisions need to be put in place.

Plans for the next versions of this screen saver:

1. It might be fun to add a variety of electric fields over all this action, static or oscillatory.
2. I'm going to add some transparent charts giving information about statistical attributes of the group as a whole. Things like energy, momentum distribution, and entropy of the system, etc. Ideally, I'd like to be able to produce and track phase transitions.
3. Making charges bond to make pseudo-molecules/atoms. I'm planning on having them keep their dipole moment so that they have the possibility to make larger molecules, but it'll be interesting to see if that happens. Perhaps a Van der Waals-like force in there.
4. Maybe make a random weight distribution. Currently all objects "weight" the same.
5. After 1-3 are done, I'm going to move this to a 3-d system, probably in OpenGL. (That should also means that QuartzExtreme will help out a lot.) Ideally, I'd like to be able to reproduce something like the Alder-Wainwright hard-sphere phase transition.
6. Maybe make a nice icon.

---

Comments about writing this:

Programming Cocoa/Objective-C is a gas! Highly recommended.
Special thanks to Aaron Hillegass for his book Cocoa Programming for Mac OS X.

Tools used in its creation:

• Project Builder / Interface Builder (comes free with OS X)
• Cocoa Browser (free) to quickly look up all things Cocoa
• Some of my own Perl code to glance through example source code easily (available soon)
• TextEdit for the readme file (comes free with OS X)
• Create ($) to add a few nice graphics
• Toy Viewer (free) to convert images to jpegs
• BBEdit (free/$) to make this webpage
• and DropCompress (free) to create the download images

Version History (as best I can make out)

• 1.0 — Jan, 2003: Original version for all original Mac OS X versions
• 1.1 — Apr, 2005
• 1.2 — Dec, 2012
• 1.3 — Nov, 2024: Found out what was stopping it from running on Sequoia

---

Ideas for me? Send them! I'd love to hear from you. I'd might even have time to work with anyone interested in doing (Objective-C) code on this also. Email me here.

Charged Spheres is freeware. Use it, redistribute it, pass it around, enjoy it.

-Jeff