**What is the historical background of the recent "Fractal Frenzy" in Junk DNA? **

**It is all about Geometry of Nature.
First, of Geos, the Universe, then the Brain ... and now the 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 x

(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 -----------**

**1775-1856
Farkas Bolyai** and his son

János Bolyai and

1777-1855

Johann Gauss

**------------------ SECOND "BIFURCATION" - NON-DIFFERENTIABLE GEOMETRIES APPEAR, -----------**

**1831-1889
duBois Reymond** blows open the field by proving continuous nondifferentiable function constructed by Weierstrass

**1845-1918
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-----------**

**1864-1907
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

**1868-1942
Hausdorff**-dimension gave quantitative measure of non-integer dimension.

**1875-1941
Lebesgue** contributes with the "Lebesgue measure"

**1902-1950
Zipf**, with "Zipf's law" lays the rules of repetition

**1904
Koch** -curve, the cardinally simple graph, based on recursive instructions

**1879-1955
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-----------**

**1901-1976
Heisenberg
1887-1961 Schrödinger
**Establish quantum-mechanics, deviating from smooth-differentiable manifolds to generate the intrinsic mathematics for nuclear physics

**1955
**

**1955
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-----------**

**1953
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.

**1977
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".

**1975-1977**

**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

**1987
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.

**1989
Pellionisz **establishes that neurons of the brain (the Purkinje cell of the cerebellum) is best modelled by Fractal Geometry.

**2002
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"**

**WWW.FRACTAL.ORG****
**Jules Ruis' amazingly comprehensive "hub" of fractals

**Junk DNA and Fractal Centers**

**HelixoMetry, Inc, FractoGene (Patent Pending), Silicon Valley, USA (Dr. András Pellionisz)**

**The Hunt Laboratory, UC San Francisco, USA (Dr. Anthony Hunt)**

**Haplomics, Inc., Australia (Dr. Malcolm J. Simons)**

**Fractal EU Competence Centre, The Netherlands, West Europe (Dr. Jules Ruis)**

**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

**Fractal Links**

A very comprehensive collection of fractal links - Persons and Institutions