Emergence

In any number of both theoretical and practical contexts, if a system is governed by a limited set of rules, the result of the system's rules can combine to create a greater pattern. The qualities of the patterns that emerge are consistent with the rules of the system, however this Emergent Behavior does not need to be specified in the original set of rules.

The textbook example for emergent behavior in systems with limited internal rules is that of the Game of Life, a mathematical model first proposed by British Mathematician John Horton Conway.

The Game of Life, seen below begins by placing yellow squares at random intervals on a grid of arbitrary dimensions. After placing the initial squares, we push the "Play" button and the computer then calculates the next generation of board layout by making calculations on the current generation. For every space on the borad, we apply the following rules, in order to determine whether that square will be 'on' [yellow] or 'off' [grey] in the next generation:

For a space that is 'on', 'full', or 'populated':
Each cell with one or no neighbors if turned off.
Each cell with four or more neighbors also turns off.
Each cell with two or three neighbors remains on.

For a space that is ''off', empty' or 'unpopulated'
Each cell with three neighbors 'on', will itself turn on.

Use you mouse to turn squares 'on' across the board; press play to begin calculating generations; during the calculation, you mayu click the screen to turn other cells 'on' and the results will affect the next generation:

The above application was written by Edwin Martin (http://www.bitstorm.org/gameoflife/).

 


 

In experimenting with the appicaion for a brief while, we begin to see that certain initial patterns will produce persistent patterns; some forms oscillate, others move across the screen, and some initial shapes quickly disappear:

So we can see that the rules of the system set the stage for a series of behaviors and properties that were not pspecified in the original rules of the system but nonetheless abides by these rules. The rules of the system dictate behaviors exclusively for a single cell. The emergent behaviors of the system extned the logic of the system by creating a group of corollaries, drawing from how groups and collections of cells interact.

In this way, the rules of the Game of Life can be rethought to reflect one cell's ability to survive based on the 'resource' that cell has in its neighbouring cells:

For a space that is 'on', 'full', or 'populated':
Each cell with one or no neighbors if turned off- is akin to saying that the cell 'dies' due to lack of 'resource'.
Each cell with four or more neighbors also turns off- is like saying that this cell 'dies' due to an excess of demand for resources; scarcity due to overpopulation.
Each cell with two or three neighbors remains on- suggesting a sustainable balance between 'on' and 'off', presence and absence in equilibrium.


We can now see that extraordinary patterns can emerge from a simple set of laws. Expect that this idea will be of great consequence when we consider why the Golden Spiral and the Fibonacci Sequence appears ubiquitously throughout nature.\

In order to set the stage for this, we need to delve back into the laws of thermodynamics, in order to understand the rules that govern the combination and recombination of matter. Taking these general rules and then examining the current sstate of the universe, we lay the groundwork for the Universe as a self-organizing system.

 

Thermodynamics, Number Theory and The Goilden Ratio
Creation, Evolution and the Golden Rule
Theory of Order
Why Fibonacci and Gibonacci sequences appear everywhere in nature,
and how simple combinatoric math can describe how a Universe with simple beginnings evolved into a complex form