#E1523D

$John Arden Hiigli. Chrome 194, 2011 Transparent Oil on Linen Canvas Through a process known as subdivision a tetrahedron can be broken down to infinity. Subdivision produces the cyclical growth of other structures, such as the cube octahedron (CUO). The lowest frequency tetrahedron capable of “growing” a cube octahedron is the four-frequency tetrahedron. The eight-frequency tetrahedron produces a two-frequency cube octahedron as well. The sixteen-frequency tetrahedron produces a nuclear CUO, a nuclear two-frequency CUO and a nuclear four-frequency CUO. Thus we can say that the sub-division of polyhedra manifests a natural space characterized by transformation and change of scale. Scale change involves systems in which the size of individual forms vary incessantly while the proportions and characteristic shapes of these forms remain constant. These forms and their proportions can be grouped in a regular sequence in which the elements of the sequence constitute an infinite series. Such “scale-invariant” sequences occur in nature (the leaf’s nervure, the laceration of the fern, the widening or narrowing line of the snail shell, the shoreline of the continents, etc). This “invariability” is also a characteristic of fractal geometry. In the Isotropic Vector Matrix the potential for scale change is related to infinite transformation. With every doubling (or halving) of edge-length the volume increases (or decreases) by eight (8), equivalent to the octave in music. The artistic strategy of using transparent oil paint makes it possible to explore and communicate this world of higher dimensions. Scale shifting, or scale change, as well as the repetitious logic enabling it, is known in mathematics as “iteration,” hence the term “iterative mathematics/geometry”. It is a particular feature of IVM that is a useful tool in both mathematics and art education. In particular scale change provides a tool of measurement with which to evaluate angle & distance information. via: bridges math art$

John Arden Hiigli. Chrome 194, 2011
Transparent Oil on Linen Canvas

Through a process known as subdivision a tetrahedron can be broken down to infinity. Subdivision produces the cyclical growth of other structures, such as the cube octahedron (CUO). The lowest frequency tetrahedron capable of “growing” a cube octahedron is the four-frequency tetrahedron. The eight-frequency tetrahedron produces a two-frequency cube octahedron as well. The sixteen-frequency tetrahedron produces a nuclear CUO, a nuclear two-frequency CUO and a nuclear four-frequency CUO. Thus we can say that the sub-division of polyhedra manifests a natural space characterized by transformation and change of scale. Scale change involves systems in which the size of individual forms vary incessantly while the proportions and characteristic shapes of these forms remain constant. These forms and their proportions can be grouped in a regular sequence in which the elements of the sequence constitute an infinite series. Such “scale-invariant” sequences occur in nature (the leaf’s nervure, the laceration of the fern, the widening or narrowing line of the snail shell, the shoreline of the continents, etc). This “invariability” is also a characteristic of fractal geometry. In the Isotropic Vector Matrix the potential for scale change is related to infinite transformation. With every doubling (or halving) of edge-length the volume increases (or decreases) by eight (8), equivalent to the octave in music. The artistic strategy of using transparent oil paint makes it possible to explore and communicate this world of higher dimensions. Scale shifting, or scale change, as well as the repetitious logic enabling it, is known in mathematics as “iteration,” hence the term “iterative mathematics/geometry”. It is a particular feature of IVM that is a useful tool in both mathematics and art education. In particular scale change provides a tool of measurement with which to evaluate angle & distance information.

via: bridges math art

Jan Tschichold Die neue Typographie, 1928

“The ‘form’ of the New Typography is also a spiritual expression of our world-view. It is necessary therefore first of all to learn how to understand its principles, if one wishes to judge them correctly or oneself design within their spirit.”

“The illustrations in this book, with few exceptions examples of practical work, prove that the concepts of the New Typography, in use, allow us for the first time to meet the demands of our age for purity, clarity, fitness for purpose, and totality.” (ibid.)

“Modern man, whose vision of the world is collective-total, no longer individual-specialist, needs no special reminder of the rightness of being closely aware of such related activities as modern painting and photography. I therefore thought it desirable to say something more about this new way of viewing our world, in which our spiritual conception of the new forms are linked with the whole range of human activity.”

Photos via: burningsettlerscabin

A4-sized poster filled with the first 10,000 decimals of phi.

Ideia Visivel, 1956 by Waldemar Cordeiro

Source: darksilenceinsuburbia

Fivefold and Spiral Symmetry Associated with Fibonacci Sequence

found: here

theshipthatflew:

The acanthus, full size, from a photograph, 1910, from The grammar of ornament : illustrated by examples from various styles of ornament, one hundred and twelve plates. Bernard Quaritch, Jones, Owen (1809-1874)

Source: theshipthatflew

A. M. Selvam

The Fibonacci spiral is traced with mathematical precision in nature in the dynamical growth processes of plants as seen in the geometrical placement on the shoot, of primordia, which later develop into the various plant parts. In a majority (92%) of plants studied world wide, successive primordia always subtend angle equal to the golden angle at the apical center (Jean, 1994 References). Primordia placement in space and time may therefore be resolved into the precise geometrical pattern of the quasiperiodic Penrose tiling pattern.

found: here