Friday, April 22, 2011

Luck, Destiny and Environment in Life: A Comparison With Algorithmic Trees Generated With LindenMayer Systems

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

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 with Lindenmayer systems:
Lindenmayer systems are algorithms that are able to generate very realistic-looking trees. If you look at a tree, they are not regular in shape and yet our eyes see a natural kind of symmetry in each tree, and this translates into Beauty. Nature's symmetry is Fractal symmetry and consists of the iteration of simple rules to create complex structures. These rules were discovered by Aristid Lindemayer, a Hungarian botanist and his partner Przemyslaw Prusinkiwicz in the book "The Algorithmic Beauty of Plants". The power of modern computers enable us to generate plant-like images from Lindenmayer's rules. An example of a rule is:

Example 8: Fractal plant

variables : X F
constants : + −
start : X
rules : (X → F-[[X]+X]+F[+FX]-X), (F → FF)
angle : 25°

Here, F means "draw forward", - means "turn left 25°", and + means "turn right 25°". X does not correspond to any drawing action and is used to control the evolution of the curve. [ corresponds to saving the current values for position and angle, which are restored when the corresponding ] is executed. Those who are familiar with Turtle graphics will see that these plan algorithms are very simple and clear. As in all complex systems, there are a lot of variations and Lindenmayer's book " The Algorithmic Beauty of Plants give the details to accommodate these variations into the general system.

* the above taken from Wikipedia.
Thus how a tree grows to look like depends very much on its initial specifications as given by the number of variables, and the constants which inter-act with them, as well as the angle for 'turns' at each point of growth. By varying angles, initial thickness of stems, and speed and intensity of growth, the shape of different trees 'of the same species' can vary quite a lot. And yet they all bear the unmistakable identity of the species. The images above were generated with different initial specifications and iterated for up to 10 generations. * here, I must qualify that a small number of individuals do manage to cross boundaries and 'become' another species e.g.
In the analogy with life, you may be born an unfortunate species. And yet within your boundary, there is much leeway for you to change your shape. In the context of the modern world, factors which will enable you to produce the greatest change within your boundary are:
1. Networking: widen your networks beyond your normal circle of friends and work contacts. If you study the theory of Networks you find that in all networks, a very small number of nodes have the greatest concentration of connections and dominate the network in terms of impact. Be one of those nodes. Also not that network connections grow exponentially.
2. Leverage the use of the Internet to be global and 'scaleable' and reap the returns of exponential feedback effects.
3. Seize opportunities offered by random unforeseen events especially those of a Black Swan type i.e. improbable events which have high impact. Better still, expose yourself to be more likely to meet Black Swans.
Note: Black Swans are the Black Swans of Naseem Nicholas Taleb's book " The Black Swan" and not the Black Swan of the film starring Natalie Portman.

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