What is the historical background of the recent "Fractal Frenzy" in Junk DNA?
Actually, the story of "Geometry" is at least 2500 years long, with the last 200 years increasingly accelerating. The last chapters became even "hurried" under the extraordinary pressures; going for nuclear energy, computational ballistics, information geometry of brain function, control of fighter jets by neural nets - and recently escalated for personalized medicine
569 BC - 475 BC
Pythagoras. Theorem of Pythagoras'
Greek "Geometer", Samos, Ionia
Distance measure in flat geometries (e.g. a surface) is x2 + y2 = d2
(Theorem of Pythagoras' - middle school today)
324 - 265 BC
Euclid (Elements). Mathematical Language of Nature by Euclidean "Geo-Metry" is over 2000 years old.
Measured land (flat 2-dimensional surfaces of Geos) in Egypt (Alexandria).
1596 - 1650
Descartes associates Brain Function with internal representation in Euclidean Geometry
1642 - 11727
Isaac Newton establishes physics and mechanics based on Euclidean Geometry
------------------ FIRST "BIFURCATION" - BREAKING AWAY FROM EUCLIDEAN GEOMETRIES -----------
Farkas Bolyai and his son
János Bolyai and
collectively establish the hard mathematical core, that "Alternative Geometries" to Euclidean axioms are equally possible
------------------ SECOND "BIFURCATION" - NON-DIFFERENTIABLE GEOMETRIES APPEAR, -----------
duBois Reymond blows open the field by proving continuous nondifferentiable function constructed by Weierstrass
Cantor set theory - an early predecessor of self-similarity theories - a core notion to later "fractals"
------------------ THIRD "BIFURCATION" - CURVED GEOMETRY OF SPACETIME MANIFOLD TO SERVE PHYSICS OF UNIVERSE-----------
Minkowski established that space and time form a 4-dimensional manifold with a unified geometry. Euclidean separable x,y,z and t are blown away
Hausdorff-dimension gave quantitative measure of non-integer dimension.
Lebesgue contributes with the "Lebesgue measure"
Zipf, with "Zipf's law" lays the rules of repetition
Koch -curve, the cardinally simple graph, based on recursive instructions
Albert Einstein established that the metric tensor of the spacetime continuum is not uniform, the spacetime manifold is curved
------------------ FOURTH "BIFURCATION" - QUANTUM MECHANICS TAKES OFF TO SERVE NUCLEAR PHYSICS-----------
Establish quantum-mechanics, deviating from smooth-differentiable manifolds to generate the intrinsic mathematics for nuclear physics
Shannon information theorist deciphers military encryption
Johnny von Neumann, done with von Neumann Algebra, declares that the intrinsic mathematics of brain function is unknown
------------------ FIFTH "BIFURCATION" - DISCOVERY OF DOUBLE HELIX IMPLIES THAT "HELIXO"-METRY WILL BE NECESSITATED, AS EUCLIDEAN "GEO"-METRY IS UNLIKELY TO SUFFICE FOR DNA-----------
Francis Crick and James Watson discover the extrinsic geometry of the Genome: the Double Helix. Have the book with all ACTG letters. What does it say? In what language? Where is the code-book? What is the encryption-algorithm? Francis Crick turns later to Neural Networks for some answers.
Genentech, inc. is incorporated in Silicon Valley. Going for the "silver bullets" of medicine, just like starting to build a thermonuclear bomb before the physics is done. The pressure is "on".
Fractal Geometry of Nature
Prof. Benoit Mandelbrot's classic book, coining the term "fractal", establishing fractal art, and hinting that neurons might be fractal-like
Pellionisz establishes that the Sensorimotor Neural Networks (such as the Cerebellum) embedd the external Minkowski space-time into multidimensional (overcomplete) neural manifolds with grossly non-Euclidean metric tensor.
Pellionisz establishes that neurons of the brain (the Purkinje cell of the cerebellum) is best modelled by Fractal Geometry.
Pellionisz submits USA Patent Application (FractoGene), claiming applications on causal relationship between the DNA coding in terms of Fractal Geometry the living organisms with Fractal Structuro-functional properties.
Best "Fractal Hub"
Jules Ruis' amazingly comprehensive "hub" of fractals
Junk DNA and Fractal Centers
More Fractal Links
Topology and geometry of fractals
An excellent mathematical perspective on applications of fractals by Michael Barnsley
Thomas Marsh and Jan Hubicka
Great art gallery, 2D and 3D, animations
Fractal data compression
Michael Barnsley: on hitherto the far most useful application of fractal geometry
A slew of "classic fractal leaders" - together
Peitgen's beautiful collection of fractal art from leaders of fractals
Complex adaptive systems.
A fantastic collection or classic fractal books, Chaos, Fractals, Nanotechnology, Fractal art
A very comprehensive collection of fractal links - Persons and Institutions