Patterns out of Randomness

When there is more than one good answer.

You are eating an apple. When does the apple cease being an apple and becomes just a core with a few seeds?

Life is a meta-pattern of patterns interacting with patterns.

Positive feedback messes up theories. It gives problems so many variables that we used to ignore it to avoid the hassles.

We usually see non-linear systems as fractals. Fractal is a name coined by a fellow by the name of Mandelbrot in the 1960's. Fractals are the branch of geometry dealing with 'broken curves'. Remember that nonlinear problems have graphs that have strange and unusual lines or ... 'broken curves'. There are two approaches to fractals: the natural lines (Has anyone ever seen a truly straight line or perfect curve in any natural object?) and the theoretical mathematical constructions.

Wolfram showed that similar rules give similar results and dissimilar rules give different results.

How many successful animals are there that eat grass?

The Game of Life is over twenty-five years old. The original rules were designed by a mathematician by the name of John Conway and his students. You play the game on a grid of square cells that stretches in all directions to infinity. The game is a balancing act between life and death. A cell is alive if something is in it. Around each cell are its eight neighbors (four sides and four corners) that are either occupied by life or empty. If during a period of play, the occupied cell has exactly two neighbors everything stays the same. If three living cells surround an empty cell, they produce new life in the empty cell. If a living cell has four or more living neighbors, it dies of overcrowding. A cell also dies of loneliness if it has no neighbors or only one. All the births and deaths occur during the same generation or period of time. In the following period the life and death of cells are again decided. The game is started when a pattern of living cells is introduced on the grid. The game will then play itself over successive periods or generations until it is stopped.

Why are there two kinds of planets in the solar system, gas and solid?

Why do clocks go clockwise? Why don't they go in both directions? At one time they did. The first mechanical clocks were the size of small buildings. Towns would build a clock for the prestige. One builder made a design that other towns copied. It happened to go clockwise. Soon every clock in Europe went clockwise. European traders traveled the world. Their navigational aid was the clock. The clock was copied everywhere they went. The world only has clockwise clocks now. Positive feedback!

The less accurately you know something the more you know!

The Mandelbrot curve is called by some the most complex curve in the world. It is a one-dimensional line that is so broken that it becomes a two-dimensional object.

Bifurcation is when something breaks down into another pattern. At one time it was called catastrophe theory.

The name fuzzy logic was first used by Lofti Zadeh in the 1960's. He used the name as a challenge to the logic that the Western civilizations have used since the time of Aristotle. The ideas of fuzzy logic have been around for years. What is new is the formalization of these ideas into a mathematical type discipline that can be used to solve problems.

Frost on the window is a pattern that is random.

Genetic machines and programs are techniques to find answers to complex problems. The programs are made with objects that can be mixed. Successful programs are allowed to mix or breed resulting in better programs.

A neural net is just a feedback net with a set of nodes.

The population problem is mathematical way to see the effects of feedback.

A man by the name of Feigenbaum discovered that the distance between each bifurcation follows a simple ratio. The ratio or distance is 1/4.669.

Mathematics is the language of patterns and therefore the language of life, but it is fuzzy!

When chaos collapses you get complexity!

The Golden Ratio or the Fibonacci sequence mimics natural patterns.

The Turing machine can be considered a special case of the Game of Life played out with the rules of mathematics.

An airplane doesn't flap its wings because the rules of airplane mechanics are not the same as the rules for living flight.