Fractal Geometry 39th Day 02-08

by Administrator 8. February 2011 03:28


“Benoit Mandelbrot known as a father of fractal geometry was a true visionary and maverick. His book “The Fractal Geometry of Nature” sparked wide spread of interest in fractals and contributed to chaos theory and other fields of science and mathematics.”

 “ A fractal is a rough or fragmented geometric shape that can be split into parts, each of which is a reduced size copy of the whole “ by Wikipedia .

       Natural fractals include shape of the mountains, coastlines, river basins, structure of plants, blood vessels, lungs, clustering of galaxies, shape of the shells, crystal growth…. “Clouds are not spheres, mountains are not cones, coastlines are not circle, and bark is not smooth, nor does lightning travel in the straight line “          Mandelbrot in his introduction to The Fractals Geometry of Nature.

 Many things in nature thought of as chaos are just following fractal laws of behavior. So many things turned out to be fractals, that the word “chaos”( in science) has redefined. Perfect example of fractal, would be the picture of the fern.  We can duplicate the shape of the fern by generating random numbers and placing them on the grid. After few dozens of repetitions the shape of perfect ferns appears…out of abstract world of math. How is it possible? Simply is…. Nature follows the simplest and most efficient path.

Human beings always searched for the answers and the definitions of who they are…. Psychologists tried to established certain theories, explain how we act and relate to the outside world. I could never accept the simple cut and paste attitude in evaluating people, full of perfect squares and triangles …feeling so unnatural and stiffed in its vision.

 Let’s think for a moment about an idea of introvert and extrovert.

The academic distinction, between basic types in human psychology presented me with more questions than answers. I could clearly find both characteristics in the same person, highlighted and brought forward at different times throughout their life. The rigid distinction, in psychological characterization is not the first one, reminding me of the “square thinking” and sterile fitting into “man made”, right angles molds. I understand, it is easier to simplify some concepts, but assigning us to only one type, will not allowed, to show richness and complexity of our personalities.

In psychological sense, the delicate balance of the introvert and extrovert in all of us, acts as a stabilizer to monitor the incoming and outgoing information. It reminds me of the single cell structure with cell membrane controlling movement of substances in and out, to create life and balance.

 The ratio of the new information, from the outside world, and the “absorbed” one (being part of us) , could be the results of the individual choice, or maybe the …. “fractal” factor…. ?  The “random”( in our perception)  law of smooth coexisting between those  two elements, in seemingly chaotic proportion, could be …..the Nature in working.  After all we are part of this world. Only, our “old perception,” based in the Euclidean geometry….doesn’t allow us to see possibility of fractal application in psychology.

Most people define themselves as the extrovert or introvert by showing majority of the characteristics of one or another. Extroverts tend to be assertive, gregarious, seeking excitement and introverts are more reserved, less sociable or outgoing.

I’ve noticed some people, attempting to be careful in monitoring of their actions, to “stick” to the defined set of behavior, in belief to be true to themselves. They were told or perceived themselves, as the introvert or extrovert, and later on in life….very rarely would they venture to the “other side”. My question is why not? Living accordingly to scripted recipe of “who I am”, and not “checking the pulse” in the present moment is the very limited vision. Making sure we match the “blue prints”, instead of creating the fresh, better fitting and reflecting the constant change is self defeating.

 The idea of searching and finding your true self and then putting it in the pre fabricated, ill fit…..classical geometry, “box”…doesn’t make much sense ….. It’s like fitting the ball to the square box.

The sad fact is that we may live our whole life, not even trying to discover the best, suitable “shape” for us. Categorizing before exploring is like making up your mind before seeing all the data.  I would strongly encourage everyone to try to live “out of the box” and not to settle for the superficial form. Just because you are the quiet and reserved “fellow”, it doesn’t mean you can’t be the life of the party. On the other hand the dynamic and chatty girl may surprise us, with deeply thoughtful disposition.

Long time ago it occurred to me, I needed both elements to stay healthy and happy. There were the  times of my life, lived as an extrovert. It seems, I couldn’t get enough of social interactions, ways to communicate, expand, and share the information with the world. Wanted to be busy in my physical actions, all the thinking process was on the outside….as in “what you see is what you get”. Other times, I wanted to have a quiet and undisturbed life, full of accumulating, through reading, thinking, reflecting. Time of stillness  and internal concentration…maybe redefining my goals, finding inner connections …..and possibly checking the authenticity of the “ inner self”. One without another couldn’t fully exist, as in waves and cycles in life….expansion and absorption of information with redefining and processing in the middle.

I would love to see people, not accepting the “ready made cages” for themselves. Finding your own self, as an individual, not the statistical occurrence or possibility. Trusting the intuition in  defining the “unique, own shape” of existence and limits. Not giving away the right, to create the true self and not settling for prefabricated and generic version of “you”.




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The Little Prince

"People where you live," the little prince said, "grow five thousand roses in one garden... yet they don't find what they're looking for..."

"They don't find it," I answered.

"And yet what they're looking for could be found in a single rose, or a little water..."

"Of course," I answered.

And the little prince added, "But eyes are blind. You have to look with the heart."








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