After a long term love affair with modular structures in art, design and nature which came to include an exploration of Vedic mathematics, Hindu mandalas, Islamic pattern, various ancient and modern cosmologies and our physiological and cognitive responses to pattern, I was driven to further explore the relationships between the elements of number, the structures thus described and/or generated and our evolving multidimensional models of reality which include the aesthetic and ethical dimensions]. It has become increasingly evident that It [all] reveals itself as a game with a set of essentially simple rules.

Whether or not the set of rules with their power to generate the richness and diversity that we experience is real, is actually under pinning the phenomenological world or is created by us to make sense of It All is of course the big question that enthrals so many of us.

We all seek insight, we are all potential Seers - see-ers, visionaries.

There are some key principles which together inform this work, most of which are generally accepted in all walks of life [perhaps a more meaningful phrase in the context of The Game of Life].

2.0.1. Key Principles

  • Metaphor and analogy are key aids to insight
  • From simple rules emerge complex consequences
  • Constraint encourages creativity
  • A game without rules is short lived
  • Autonomy is illusory - everything is interdependent [....in a continuum of space, time and matter formed in and by hierarchies of varied complexity]
  • Things are determined by relationships
  • Relationships depend on communication
  • We live on the Edge of Chaos
  • 2.1 Nature

    2.1.1 Philomorphs.

    2.1.2 The Growth Pattern of Hexagons - Counting each stage of growth and reducing totals to single, colour coded digits reveals a distinctive pattern.

    2.1.3 The Growth Pattern of Triangles - Counting each stage of growth and reducing totals to single, colour coded digits reveals a distinctive pattern.

    2.1.4 Unfolding Digits as Polygons - Shows not only the growth pattern of the polygons but also adds character to the relationship of the digits 1 - 9 [all larger numbers reduced].

    2.1.5 HIERARCHICAL ORDERS [after J.L.Jolley - The Fabric of Knowledge. London and New York 1973] - Is an example of how we use lists of concepts rather like we use number and vice versa.

    2.1.6 The fractal cabbage [This and the following Images from Nature are examples of geometry in nature and illustrate the sense of satisfaction gained from observing self similarity in nature.]

    2.1.7 The self similar cauliflower.

    2.1.8 Crystal geometry - Basalt.

    2.1.9 Form generated by vibrating powder [similar to the underside of a cowrie shell!]From Cymatics by Hans Jenny Basle - 1967.

    2.1.10 Desert Rose - Calcite, formed under the sand of the Sahara.

    2.1.11 Good Vibrations - Different notes create different patterns in powder on the skins of the kettle drums.

    2.1.12 Self similar structure in leaves.

    2.1.13 Water Lilly - Geometry in nature.

    2.1.14 Succulent - As leaves grow from the centre, the plane distorts.

    2.1.15 Rhododendron - Almost forms a dodecahedron of pentagonal florets.

    2.1.16 Nebulae - Similar patterns on all scales of magnitude - A self similar cosmos.

    2.2 Art - From earliest times number, nature and art have been entwined in the mind of mankind. This and the following images from art are examples of geometry in art and illustrate the sense of satisfaction gained from observing self similarity in art as in and from nature.]

    2.2.1 The Dream of the Great Ennead.

    2.2.2 The Great Ennead of Heliopolis.

    2.2.3 Drawing by a young, disturbed girl patterns to reinforce her understanding.

    2.2.4 Rock carving from prehistoric site in Malta.

    2.2.5 Tile pattern illustrates the found geometry of nature in art from Mosque in Isfahan, Iran.

    2.2.6 Painting by Mondrian - A modulor composition.

    2.2.7 Mandala from North India based on a 9 x 9 square.

    2.2.8 Painting by Samuel Palmer uses self similarity in composition.

    2.2.9 Mans answer to the bubble - Geodesic dome invented by Buckminster Fuller, U.S.A.

    2.2.10 Painting by Fra Angelica - Geometry in composition.

    2.2.11 Interior of conical dome in the Alhambra, Spain.

    2.2.12 Le Corbusier used his Modular system in the composition of his buildings.

    2.2.13 Gaudi worked from nature to evolve his architecture.

    2.2.14 The Greeks used the Golden Mean to maintain their compositions.

    2.3 Number.

    The power of number to model not only the appearance of things and events but also to predict their behaviour raises the question as to whether number is an invention, or a discovery by man of some aspect of the deep structure of the cosmos. Notes on the reduced Fibonacci Series - alternate figures in bold:

    And that is only the beginning ........ take the two halves and see the symmetry............

    1 3 8 3 1 and 8 6 1 6 8 or 1 2 5 4 7 8 and 8 7 4 5 2 1 etc.,etc.....................................................................................................

    Even the digits 1 - 9 show some intriguing symmetries:

    2.3.1 The full numbers 1 - 225 laid out in modulo 9 and colour coded to reveal the patterns of the reduced versions [e.g. 225 = 9 i.e. 2+2+5=9]etc.

    2.3.2 The positions and patterns of the Prime Numbers.

    2.3.3 Even numbers which when reduced show a distinctive set of relationships.

    2.3.4 Odd numbers which when reduced show a distinctive set of relationships.

    2.3.5 The Sum groups of Odd and Even numbers reduced.

    2.3.6 Games with the Magic Sevenths - The Dance of the Digits.

    2.3.7 Nines and Scherezade [After Buckminster Fuller, Synergetics].

    2.3.8 Nine points on a circle demonstrate some of the relationships of digits to be explored later.

    2.3.9 Odd behaviour in relationships can throw up distinct patterns.

    2.3.10 The Table of Powers with all numbers reduced to digits shows patterns.

    2.3.11 Some qualitative aspects of the Digits and an introduction to Digitos [a sort of domino].

    2.3.12 Games with Digitos.

    2.3.13 Sums with Digitos.

    2.3.14 Digit, Digito, and Bars.

    2.3.15 Star Nonagons, Digitos and Bars.

    2.3.16 Overlays/sums of pairs of Star Nonagons and Digitos [illustrating the duals within the digits 1 - 9, i.e. 1+8, 2+7, 3+6 and 4+5 all=9].

    2.4 The Rules of The Game Introduction

    2.4.1 The Rules.

    2.4.2 Key Concept FROM ONE TO EIGHT AND NINE ........... IN COLOUR .

    2.4.3 The COLOUR Cube [The sum of whose diagonals = 9 [the complementaries].

    2.4.4 The COLOUR Nonagon.

    2.4.5 Some thoughts on Measure [Definition: an action to achieve a purpose - a slow and stately dance...].

    2.4.6 A COLOUR Circle.

    2.4.7 Key set - A summary sheet of digit, colour, bars, digitos etc.

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