John Horton Conway’s Game of Life

A period-29 Oscillator in the Game of Life

I have always been fascinated by cellular automata, specifically the brand governed by the rules devised by the mathematician John Horton Conway, which is known as the Game of Life.

What I find particularly fascinating is the fact that such simple rules give rise to such complex behaviors.  The Game is played this way:

There exists a grid of squares, each of which can be in one of two states: ON or OFF.  The rules for changing states are simple and depend only on the states of the square’s 8 nearest neighbors.

  1. An ON cell with fewer than two ON neighbours turns OFF.
  2. An ON cell with more than three ON neighbours turns OFF.
  3. An OFF cell with exactly three ON neighbours turns ON.

One can think of the first rule as stating that the cell dies from loneliness.  In the second rule, the cell dies from overcrowding.  To come to life, you need exactly three neighbors.  Here is a link to the original Scientific American article from 1970.

Since each cell has eight possible neighbors, but can only stay on if it has one or two ON neighbors, the playing field will be rather sparse.  The situation is rather unstable since three ON neighbors can turn ON a cell, but this increases the chances that another ON cell will now have more than three ON neighbors, which would make it turn OFF.  In that event, life would lead to death.  In a generic sparse environment, the tendency is to grow, but this leads to a crowded environment where the tendency is to diminish.  The general result is that the playing field will be mostly empty with pockets of ON cells evolving dynamically.

This game is an excellent example of how simple rules can lead to extremely complex behavior.

To play, you can check out an online applet, or download your own superfast game from Golly Game of Life.  The latter is very nice as you can choose from a host of fascinating patterns to load and play with.

One can go to Stephen Silver’s Life Lexicon to see a library (or bestiary) of most of the known creatures.

Above is an emblem I created in Mathematica that is a period-29 oscillator.  That is, the pattern repeats every 29 steps.  I had previously used it on a website for a course on complex systems that I taught at CUNY in 1998.

Kevin Knuth
Albany NY

Arthur C. Clarke’s Last Interview

IEEE Spectrum radio has on audio podcast the last interview with Arthur C. Clarke.

Futurist and science fiction author, Sir Arthur C. Clarke (1917-2008) created 2001: A Space Odyssey, as well as envisioning using geosynchronous satellites for global communication. He is also a huge proponent of the Space Elevator, and says that we will start building it 10 years after everyone stops laughing. He is probably right.

The Arthur C. Clarke Foundation continues to promote his vision.

Kevin Knuth
Albany NY

Making Things Talk

Looking back, I am surprised at how electronics has quietly advanced to the point where we can buy small programmable computers on chips for a dollar or two.  These are microcontrollers of course, and in my lab we are working on programming them to handle the tedious tasks in our robotics projects.

At, I stumbled on this gem of a book titled “Making Things Talk

It is packed with 26 electronics projects that involve getting these tiny computers to talk to each other and the internet over both wired and wireless connections.  I have ordered all the requisite parts, and when purchased, they amount to around $280.  I am looking forward to summer vacation when I get to go through each of these projects one-by-one:

  1. Making a computer “mouse” out of a stuffed animal monkey and flex sensors.
  2. Making the monkey wireless
  3. Negotiating in Bluetooth with the BlueSMiRF module
  4. Setting up a networked webcam
  5. Connecting a microcontroller to the internet without a computer
  6. Networked Air Quality Meter
  7. Networked Games
  8. Infrared Communication
  9. Radio Communication
  10. Duplex Radio Communication
  11. Bluetooth Communication
  12. Broadcasting Messaging
  13. Directed Messaging
  14. Infrared Rangefinding
  15. Ultrasonic Rangefinding
  16. Reading Signal Strength with XBee Radios
  17. Reading Signal Strength with Bluetooth Radios
  18. Reading the GPS Serial Protocol
  19. Heading with a Digital Compass
  20. Attitude with an Accelerometer
  21. Color Recognition with a Webcam
  22. 2D Barcode Recognition with a Webcam
  23. Reading RFID Tags
  24. RFID and Home Automation
  25. IP Geocoding
  26. Email from RFID

OK, I wont be making each of these.  I will get an idea halfway through and take off and work on that.  But it should be fun!

Kevin Knuth
Albany NY