寻找隐秘的维度

这世界，太多的奥秘，需要去探索
数学，本身就代表着规则
而分形，则给看似无规则的自然世界一个合理的解释
这是西方人的强项

以分形理论来说，fractal could be found in everywhere

那么时候地球所在的太阳系甚至银河系也是茫茫宇宙的某个分形中的一只branch？

神奇

The film is about fractal geometry. Someone calls fractal geometry 'the natural dynamics of everything' (a video title, 2011, available at //www.youtube.com/watch?v=yUM7e0tIFi0). Why? Because it explains the shapes of everything in the nature: why the British coastline looks like that, why mountains looks like that, why the trees look like that, why the vessels in the body look like that, ect., etc..

Fractal geometry was invented by Benoit Mandelbrot from 1950. In general, it is a combination of classical geometry (coined by Euclid) and algorithm. The most famous fractal - The Mandelbrot Set - derives from a circle and a generating function 'f(z) = z^2 + c'. (For more knowledge, visit http://mathworld.wolfram.com/MandelbrotSet.html)

In reflection, fractal geometry could help us to understand the underlying order governed by simple mathematical rules. According to this theory, there must be a rule that governs the formation of the nature and all the living things/creatures. Perhaps the rule is set by the God. God is simple, straightforward and God seems not encountered complex things, thus God create everything as they assumed to be. A significance of fractal geometry might be that it finds out the rules of the nature, which implies that the nature is possibly created and ruled by something. So far, we may easily shift our thoughts to another interesting invention in the 20th century - the Artifical Intelligence. With the emergence of computer, multiple complex things can be handled by computer programming. Some people may say, artificial intelligence is God. (see http://www.artificialintelligenceisgod.com/index3.html) If science explains the world created by God, then technology is the 'new God' that changes the existing world. Is it? If it is so, then there must be a number of Gods that mobilize the evolutions of all things in our history. On the other hand, however, like technology is rooted in science, science is rooted in the nature, and evolutions of all things are rooted in the earliest forms and the evolution of a certain thing follows a common rule. Therefore, this question seems unanswerable by philosophy of science, except acknowledging the existence of God. So I just want to stop here.

Drawing on the former argument, fractal geometry could help us to understand the underlying order governed by simple mathematical rules, I have another question: is this process reversible, i.e., could the setting of rules help generate complex ideal orders? In my own field, urban planning and design, I acknowledge that some scholars have studied how, or if it is possible, a set of simple rules may generate ideal urban form (Alexander, 1966; Marshall, 2009). However, city is formed by both controllable and uncontrollable, visible and invisible forces. And the urban form becomes more and more complex, and the urban problems continuously emerge with the increasing complexity of our society. In my view, the study of ideal urban forms, no matter by what means, is something similar to the system dynamics mentioned by Meadows et al. in their book 'The Limits to Growth' - a game of idealism.



空城
6 April, 2014
Film available at //www.youtube.com/watch?v=s65DSz78jW4 ;

Go with basic and simple purpose, conducting similarity and virable options which is callled EVOLUTION.

I do like it, from the smoothly math to the real change of the world around us. Similarity is not only a Math but sharing the same vision on physics, from Newton, to Einstein, to the parallel universe.

Loren Carpenter (visualize)-> what the planes might look like in flight.
Fractals - Form, Chance, and Dimension by Benoit Mandelbrot

It's one of the keys to fractal geometry call iteration in mathematicians.

First Mountain and then "Star Trek II" the Wrath of khan.

Self-similarity always zoom in and out the object look the same.

People like the great 19th century Japanese artist Katsushika Hokusai

the mystery of the monsters, a story really begins in later 19 century, Georg Cantor (German)
Created first monsters in 1883, call " Cantor Set."

Another by the Swedish Helge Von Koch, one of the classical Euclidean geometric figures.
in the 1940s, British Scientist Lewis Richardson,
Koch Curve he wrote a very famous article i Science Magazine called " How Long is the Coastline of British."

Dimension
French Gaston Julia

Mandelbrot in IBM

one the combined all of the Julia sets.
f(Z)=Z2+C into a single image. The Mandelbrot Set

Late 1970s, Jhane Barnes
new book "the Fractal Geometry of Nature"
1990, a Boston radio astronomer Nathan Cohen
 have been discovered back in the 1930s.

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E=M 3/4

A General Model for the origin of allometric scaling laws in Biology