Center of Complex, Simple
& Natural Studies©
PRÓXIMAMENTE EN ESPAÑOL

Centro de Estudios Complejos
Simples y Naturales©

COSMOGEOMETRY©
COSMOGEOMETRÍA©
Alejandro Franz

IF YOU ARE INTERESTED TO PARTICIPATE PLEASE CONTACT 

Alejandro Franz
director@alcione.org




Hermes Trismegistus


Geometry has two great treasures:

               One is the theorem of Pythagoras; the other,
                the division of a line into extreme and mean ratio.
                The first we may compare to a measure of gold;
                the second we may name a precious jewel."
                                 - Johannes Kepler [1571-1630]


Johannes Kepler
      Born: 27 Dec 1571 in Weil der Stadt (near Leonberg),
Holy Roman Empire (now Germany)
     Died: 15 Nov 1630 in Regensburg (now in Germany)



La Geometría tiene dos grandes tesoros:

Uno es el teorema de PITÁGORAS; el otro
la división de una linea entre un extremo y el radio medio.
Al primero lo podemos comparar a una medida de ORO
al segundo lo podemos nombrar "Una preciosa JOYA"
-- Johannes Kepler [1571-1630]


"For of three magnitudes, if the greatest (AB) is to the mean (CB) 
 and the mean (CB) is to the least (AC), they therefore all shall be one."

AB/CB = CB/AC = 1.618...



Orthophysical - Morphogenesis.
    Results obtained in the last decades in the field of the nonlinear
    approachof natural phenomena, the founding of new disciplines with
    synthesis-character like:  synergetics, complexity physics, theory of
    catastrophes,the emergence of  mathematical and geometrical models
    that are moreappropriatefor the description of the surrounding reality: 
    Fractals, Chaos Theory, as wellasthe one of Cellular Automata and of
    Neural Networks , The  Pyramids Power  made it possibleto approach,
    from a new angle of view, a domain of maximaldifficulty: the existence
    of the living and its relation with the inorganicenvironment -- a field
    synthesisingthe scientific knowledge obtained from antiquity until today.

                     Being materialized in studies and investigations in ecology,
    in biotechnology and bioengineering, in bio-geophysics and life quality,
    modern scientific research needs a specific theme structure and a specific
    methodology ,relying on the latest  achievements, as well as a proper
    organizing structure:an important part thereof is represented by the 
    developing of international,interdisciplinary research groups.

The Centre for Complex & Natural Studies
nonprofit association, having as its leading aims:

  To represent the interest of a group of people concerned with the promotion and   the development
of research in the field of  fractal physics, nonlinear dynamics,  as well as  complex systems evolving
far from thermodynamic equilibrium, Sacred  Hermetic Geometry and COSMOGEOMETRY©.

  To provide an interface between theory and application;

  To support, by means of courses, lectures, summer schools, conferences,
by publications and other audio-video media forms, a continuous information
of a large mass of young people,  in view of a generalization of an effective
communicationmode between disciplines that seem today to be distinct
and separated.
 
 

Fields of Interest & Developing Projects
Direction 1. Studies on the process of morphogenesis.

Key words: form, pattern, morphogenesis, self-organization, fractals, aggregation,
fragmentation, time series analysis, pattern analysis, industrial applications;

Theme 1. Form in nature: analysis and synthesis.

  Collection of archetypal images obtained by experiment or found in nature

Goals:
- Identification of the variability of patterns obtained in different processes
- physical, chemical,     biochemical, biological (growth of colonies of bacteria);
- Identification of specific techniques dedicated to the acquisition and the digital
   processing of     images, in view of an optimal emphasizing of the archetypal
   structure.

  Collection of archetypal images obtained by numerical modelling

Goals:
- Conception of numerical programs capable to generate geometrical structures
  similar with   images found in nature;
- Identification of the variability of patterns generated by numerical modelling.

  Complex methodology for the quantitative evaluation, classification
   and discrimination of spatial anisotropies (lines, surfaces, volumes) 

Goals:
- Creativity stimulation regarding the identification of new methods for the
   analysis and the    classification/discrimination of the forms in nature; 
- Delimitation of the applicability domains of the methodologies already
   acknowledged or  proposed for the analysis of natural forms.

Global and local anisotropy evaluation by Angle Distribution of  Percolation
Length  (ADPL) 

Theoretical and experimental delimitation of the morphogenesis process

Goals:
- Establishing of contacts to institutions and persons interested in the theoretical
   formalization  of the morphogenesis process, in view of the creation of an 
   international group, addressing this   process in the framework of a unitary
   research program;
- Defining an experimental context able to emphasize the existence of a 
   morphogenetic field   beyond the effect of the known physical fields;

Theme 2.
Features of structuring in a gradient - process properties that do not depend
upon the nature of the materials or of the implied interaction mechanisms.

Theoretical and experimental studies on the structuring by aggregation

Goals:
- Modelling of the structuring by aggregation: particle-particle, 
   particle-cluster, cluster-cluster;
- Identification of optimal methods dedicated to the evaluation
   of the aggregates' geometry;
- Identification of properties - physical, chemical, technological -
   as a function of the aggregatestructure.

--Diffusion-limited aggregation and dendritic growth...

    Diffusion-limited aggregation is a general class of behavior that underlies
    many phenomena characterized by dendritic growth, such as growth of
    frost on a windowpane, lightning and sparks, and urban growth. 
    Particles of a given ``resource'' (molecules, individuals, units of heat) diffuse
    freely until they are captured by---and contribute to the growth of---a 
    static structure. Diffusion-limited aggregation; very shallow third dimension.
Theoretical and experimental studies on the structuring by solidification 

Goals:
- Modelling of solidification phenomena;
- Identification of optimal methods dedicated to the evaluation of the
  geometry of structural anisotrophies in the solidified body;
- Identification of properties - physical, chemical, technological - 
  as a function of the chemical
  anisotropy and of the solidification defects.


        Any objective observation we make must include a discussion of 
        proportion for it is the rule of proportion in the examination of 
        nature that causes us to observe an organized universe and a 
        universe in chaos, rational and irrational numbers, harmony and 
        discord, truth and falsity. 
        These descriptions are merely proportional effects of the opposition 
        that is inherent in all things.

        We see harmony expressed by those emotions, feelings, and 
        characteristics present within ourselves.

        This harmony is viewed within nature as the Divine Proportion. 

        The Divine Proportion as scribed to our collective state of 
        observation has been expressed. 

                   "For of three magnitudes, if the greatest (AB) is to the mean (CB) 
                        and the mean (CB) is to the least (AC), they therefore all shall be one."
              AB/CB = CB/AC = 1.618...
                 The Divine Proportion was closely studied by the Greek sculptor, 
Phidias, hence, it was given the name Phi. Also known as the Golden Mean
the Magic Ratio, the Fibonacci Series, etc. 

      Phidias: 
                     Phidias (lived in 5th century BC), Greek sculptor of the classical 
      period, who was famed also as an architect and painter. 
      He was born in Attica. 
      Knowledge of his art depends on the statements of ancient writers because 
      none of his original work is believed to have survived. Athenian  statesman 
      Pericles gave Phidias his first commission, for statues to decorate Athens, 
      and made him general superintendent of all public works. 
      Phidias directed the construction of both the Parthenon and the Propylaea, 
      the monumental entrance to the Acropolis. He created the gold and ivory 
      statue of the goddess Athena that stood in the Parthenon. 
      His colossal statue of the god Zeus at Olympia 
      was considered Phidias's masterpiece. 

Phi can be found throughout the universe; from the spirals of
 Galaxies to the spiral of a Nautilus seashell; from the harmony of 

music to the beauty in art. 

            A botanist will find it in the growth  patterns of flowers and plants, 
while thezoologist sees it in the breeding of rabbits. 

         The entomologist views it in the genealogy of a bee, and the physicist observes
it in the behavior of light and atoms. 

              A Wall Street analyst finds it in the rising and falling patterns of a market, 
the mathematician in the examination of the pentagram. 

              Throughout history, Phi  has been observed to evoke emotion or  aesthetic 
feelings within the us. The ancient Egyptians used it in the construction of the great 
pyramids and in the design of  hieroglyphs found on tomb walls. 

            At another time, thousands of miles away, the ancients of Mexico embraced 
Phi while building the Sun Pyramid at Teotihuacan and many other structures 
as the  ZAPOTECA pyramids  in Tajín,Veracruz, the MAYA buildings in the 
 peninsula of  YUCATAN and many other MESO-AMERICA ancient civilizations. 

            The Greeks studied Phi closely through their mathematics and used 
it in their architecture. 

The Parthenon at Athens is a classic example of the use of the Golden Rectangle. 
 

            Plato in his Timaeus considered it the most binding of  all mathematical 
            relations and makes it the key to the physics of  the cosmos. 

        We must consider that PHI could have been originated in ATANTIS. 

         During the Renaissance, Phi served as the "hermetic"  structure on which 
         some of the great masterpieces were  composed. 
       See  Michael Maier  ATALANTA FUGIENS

            Notable artists such as Michelangelo, Raphael, and Leonardo da Vinci 
          made use of it for they knew of its appealing qualities. 

Phi must be considered in its relation to the human psyche since it is the

       psyche that interprets this phenomena. Although Phi  appears to be fixed in nature, 
       it actually is not. The only reason it seems fixed is because it is fixed within our 
      own minds. This proportion corresponds to the mental vibrations that are within us 
      and dictate our sense of pleasure and pain, beauty and ugliness, love and hate, etc. 
 

             The result is we are held captive by these memories fixed by both 
body and mind. For if we were to view nature from an altered state of 
consciousness,  the proportion would also be altered. 

               Therefore, the Divine Proportion presents itself in the very 
 physical nature of Creation. 


It is seen as the beauty and organization within the cosmos. 


THE DIVINE PROPORTION
It is the harmony and glue that holds
the unity of the Universe.
The Fibonacci Series The PRIME numbers....
                      1... 2... 3... 5... 8... 13... 21... 34... 55... 89... 144... 233...
377...610...987........etc

diagram

INSTRUCTIONS ON HOW TO OBTAIN THE
MEAN RATIO


  Theoretical and experimental studies on the structuring by fragmentation 

Goals:

- modelling of fragmentation phenomena;
- identification of optimal methods dedicated to the quantitative evaluation of
  fracturing and   fragmentation processes;
- identification of specific fingerprints linked to structuring by fragmentation.

Practical applications of pattern analysis methods in industrial processes

Fractal methods for the characterization of the quality of surfaces

Fractal methods for the characterization of fragmentation processes 
   (discrimination/classification of fragments obtained by rupture, with 
applicationsin the  investigation of industrial accidents) 

Identification of the effectiveness of fractal methods in the milling industry and the
   cement industry

Theme 3. Form: a parameter for the characterization of bodies and of their
 interactions with the environment.

The use of archetypal structures in the understanding of the unity of the material
world    (discerning the role of the form in nature)

Generalization of the Golden Cut in n-dimensional space

Identification of the golden numbers in the description of natural forms 

Theme 4. Time series analysis and synthesis.

Collection of time series obtained in physical measurements

Goals:
- Identification of the variability in the structure of time series obtained in 
   different processes
- Physical, chemical, biochemical, and the growth and the developing of the living;
- Identification of specific techniques dedicated to a preliminary digital processing,
   in view   of an optimal emphasis - in the structure of time series - of features
   representing fingerprints   of certain processes - physical, chemical, biochemical a.s.o. 

Collection of time series produced by theoretical models or in numerical
   experiments 

Goals:
- Stimulation of the creativity in the field of the generation of numerical
   programsable to produce time series;
- Identification of the variability in the structure of time series obtained by numerical
  modelling.

Complex methodology for the quantitative evaluation, classification and
   discriminationof temporal anisotropies.
   (stationary regimes, transient regimes) 

Goals:

- Creativity stimulation regarding the identification of new methods for the 
   analysisand the  classification/discrimination of time series obtained in
   measurements made on natural systems;
- Delimitation of the applicability domains of the methodologies already
  acknowledged or proposed for the analysis of time series.

Methods for the determination of the fractal character of time series
    (implications for thecognition of the model)

Direction 2. Complex studies on the living, in an Astro- geo-dynamic context. 

Key words: biostructure, metabolism, self-organization, artificial life, biological 
rhythms,  sociology, stock exchange, stock dynamics, ecology, geonomy, astrophysics. 

Theme 1. Identification of principial differences between the living and the nonliving 

Theoretical and experimental delimitation of the concept of biostructure 

Goals:
- An update of the concept of biostructure 
- Identification of methods for the experimental emphasizing of the biostructure;
- Analysis of the stability of the biostructure (influencing factors, degradation
   velocity, conservation factors).

Monitoring of biostructure quality by pattern analysis following heterogeneous 
   chemical reactions in porous media

The living - a sensor in the study of nonlinear phenomena and in the experimental
    validation of theoretical phenomenological models

Goals:

- Delimitation of the concepts: biological transducer, biological sensor and
  biosensor;
- Generation of a specific experimental context dedicated to the monitoring
  of the dynamics   and of the evolution of the living;
- Identification of the experimental context and of the specific sensor dedicated
  to the  validation of the main notions defined in the orthophysical model of the
  material world.

Theme 2. Genesis, dynamics and evolution of living hierarchic structures.

Morphogenesis and social stability - models and case studies 

Goals:
- Applying the knowledge offered by studies in the field of artificial life 
 (cellular automata,   neural automata, genetic algorithms a.s.o.) in view of the
  understanding and the modelling    of organization and self-organization of
  socialhierarchic structures (family, clan, nation,   humanity);
- Applying the methodology for measurement and classification/discrimination
- dedicated to   complex analysis of space-time anisotropies - in view of the
  objectivation of processes linked    with social structuring, with the dynamics and
  the evolution of a collectivity (society);- Implications for history, archeology,
  architecture, urbanism a.o.

Methodologies for the identification and characterization of culture types 

Characterization of the Romanian manager culture in an European and in a
    worldwide context

Management on the edge between organization and self-organization of
    economic processes 

Goals:

- Modelling the dynamics and the evolution of a hierarchic system with
  self-organization;
- Identification of the limits in which a self-organized system may be
  controlled by organization;
- Defining general rules to conduct a productive process in which the dynamics
  ofself- organization interferes with the goal stipulated by organization.

Complex methods for the analysis of stock market fluctuations and of the
   fluctuations  in the quality of work force, able to offer information to be used in 
   the manager activity

Theme 3. Delimitation and definition of the concept of 'global quality' of a
product (technical quality, biological quality, ecological quality, its integration
in the environment)
Direction 3. Studies on cognition phenomena 

Key words: cognitive sciences, neural processing, artificial intelligence, 
perception, psychology, semiotics, semantics, hermeneutics.

Theme 1. Delimiting the concept of  INFORMATION and identifying its 
                  relations with energy and matter.

Theme 2. Universality and specificity in the sensory perception.

Theme 3. Myth and its role in the perception of the world. Implications 
                  for the contemporaneous approach in research. 

Theme 4. Extrasensory perception - a modality of global information of the
                   living things. 


Fuente: Center for Complex Studies
http://www.geocities.com/Athens/4020/csc.html
© 1997 by Florin Munteanu
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