fractal reality

[AntonioLao]

McGraw-Hill’s dictionary of mathematics defines fractal as a geometric shape whose structure is such that magnification by a given factor reproduces the original object. On the other hand, Hans Lauwerier’s book entitled Fractals: Endless Repeated Geometrical Figures published by Princeton University Press in 1991begins its introduction with the following: A fractal is a geometrical figure in which an identical motif repeats itself on an ever diminishing scale. These two definitions span the entire extension between macro-cosmos and micro-cosmos of physical reality, suggesting that the existence of matter and energy including all life forms share common hidden fractal geometries. The god-father of fractals is the Franco-American mathematician Benoit B. Mandelbrot who gave the first introduction to fractals in his book: The Fractal Geometry of Nature published by Freeman in 1983.

The modern application of fractals is the design of cell-phone antennas. This design maximizes the length (which increases the bandwidth of reception and transmission of radio signals, especially in the microwave frequencies) but simultaneously minimizes the two dimensional area that keeps the compactness of each cell-phone. There are already two discoveries in mathematical research similar to fractals. These are Riemann-Weierstrass and Peano-Hilbert curves. The first is continuous but at every point it has no direction. The second fills a two-dimensional region which actually passes through every point of the region. Detailed discussions of these bizarre curves can be found in Reuben Hersh’s book: What is Mathematics, Really?On page 265 published by Oxford University Press in 1997. Life forms are observed to form similar fractal structures; a pair of eyes and a pair of ears, symmetrical numbers of limbs, a mouth, a nose with two nostrils, etc. Plants are also formed of fractals: branches and root system, leaf’s design, etc. Nevertheless, the chemical elements of the periodic table indicate the most efficient of all fractal designs: The energy levels of electronic configurations, moreover, the compositeness of hadrons, namely mesons and baryons using the fractal quarks in groups of 2 and 3, respectively. The ultimate fractal designs are the symmetric Hadamard matrices of quantized space-time.

[mkirkpatrick]

Antonio,read what Dan winter has to say about fractals and the golden mean.He is a member of toequest you can easily look him up there.

regards michael.

[AntonioLao]

I look at Dan Winter's fractal but was disappointed that he keeps referring to others' ideas but his own. For me, fractals are simply topological structures analogous to Mobius's, Hopf's, and Klein's topologies.

[mkirkpatrick]

I look at Dan Winter's fractal but was disappointed that he keeps referring to others' ideas but his own. For me, fractals are simply topological structures analogous to Mobius's, Hopf's, and Klein's topologies.

Right,thanks Antonio,I thought that he had his own theory on the matter,however I have not studied it too closely.

regards michael.

[AntonioLao]

I'm using fractals to formulate a quantum theory of space-time and hope to publish by the end of this year.

[mkirkpatrick]

I'm using fractals to formulate a quantum theory of space-time and hope to publish by the end of this year.

Wish you all the very best with your work Antonio,might even become a best seller! You could be the Steven King of the Maths world!


regards michael.

[AntonioLao]

Fractals of quantized space-time are also subjected to the law of probability similar to that found in quantum mechanics in accordance to Max Born interpretation. I'm reading a layman book on quantum mechanics by Michael D. Fayer, Ph.D. discussing how quantum theory explains our everyday world. I have read almost 6 chapters but have yet to see Fayer mentioning any form of stochastic fractals.

[mkirkpatrick]

Fractals of quantized space-time are also subjected to the law of probability similar to that found in quantum mechanics in accordance to Max Born interpretation. I'm reading a layman book on quantum mechanics by Michael D. Fayer, Ph.D. discussing how quantum theory explains our everyday world. I have read almost 6 chapters but have yet to see Fayer mentioning any form of stochastic fractals.

What then if he does not mention them at all?

regards michael.

[AntonioLao]

Thanks goodness he is not formulating a quantum theory of space-time. His book aims to make laypeople understand quantum mechanics with minimum usage of math.

[mkirkpatrick]

Thanks goodness he is not formulating a quantum theory of space-time. His book aims to make laypeople understand quantum mechanics with minimum usage of math.

Sounds just like the book I would understand.


regards michael.