ALL THINGS BIG AND SMALL 2.0

Ten Types of Common Trees In Singapore from Singapore Postage Stamp * all images generated with Fractal Grower software by Joel Castellanos of University of New Mexico: See http://www.cs.unm.edu/~joel/PaperFoldingFractal/paper.html 1. Leaves on a stem 2. Fern 3. Weed 4. Simple tree. This post is on what we often ponder: that what shapes our life as we grow is a combination of our genes, our environment, the decisions we make along the way, and random unforeseeable events which had an impact on the path we were traveling on. I choose to compare our lives with the shape of trees. An Oak is as different from a Coconut Tree as a Fern is different from a bush of Roses. An Oak cannot turn into a Coconut Tree and yet each Oak is different. The analogy with Life is that to a certain extent there is a boundary beyond which your Life cannot cross, yet within this boundary, there is considerable freedom for you to choose the the eventual 'shape' you will become. Let us illustrate this wi...

Randomness :" I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all."~~ Ecclesiastes 9:11 Non-linear Feedback Loops : “I tell you everyone who has, shall more be given, but from him who has nothing, even what he has shall be taken.” ~~Matthew 25:29 Cycles :"When the seven years of abundance enjoyed by the land of Egypt came to an end, the seven years of famine set in.."~~ Genesis 41:53/54 1. I-Dimensional Continuous Wavelet Transform of SP500 January 06-July 08 2. S&P500 Weekly Data: Jan 2006 to July 09 2008 (133 data points) 3. Wavelet-based Synthesized Time Series Example A 4. Wavelet-based Synthesized Time Series Example B 5 . Wavelet-based Synthesized Time Series Example C The reason why the stock market's direction (as represented by an Index) cannot be pr...

Images (top) self-explanatory from Charles Crowley at http://www.cs.unm.edu/~crowley/Complexity/index.html (bottom) Stephen Wolfram's four classes of cellular automata illustrating diversity with small initial differences or perturbations. Studies in Chaotic Systems, which are sub-cases of Complex Systems, show four types of movements: (1) movements that eventually become extinct of (2) movements which produce regular cycles (3) movements which grow structurally but the growth is not totally predictable (4) movements which dissolve into utter chaos. It is category 3 that is most interesting as it seems to represent the state which Life in this Universe follows and may explain how interesting, complex systems, such as living things, arise in a world where one of the most fundamental principles is that entropy, that is disorder, always increases. [Second Law of Thermodynamics]. Experiments carried out with Cellular Automata [which are grids created on a computer and populated and all...