Matrix & Octaves

Matrix is a graphic exploration of patterns in binary numbers through a series of square matrices generated by a recursive multiplication of each matrix by itself – specifically each cell of the preceding matrix is multiplied by the whole (preceding) matrix to derive the next in the series

matrix_1
matrix_2
matrix_3

Logic

The size (number of rows and columns) of each matrix is equal to the population of the preceding matrix, i.e. also square of the size of the preceding matrix. It is the series 2^(2^n) = 2; 4; 16; 256; 65,536 ... The population of the matrices is the series 2^(2^(n+1)) = 4; 16; 256; 65,536; 4,294,967,296 ...

Through the visualization of this process of progressive elaboration of the simplest originating opposition – 1 versus 0 – we are able to observe subtle patterns of repetition at different scales within the structure of the binary series.

The expansion can be calculated by:


multiplying literal values:
initially

2

(2^1), and

1

(2^0), to generate:

42
21

,

16884
8442
8442
4221

, etc.


adding powers of 2:
initially

1

and

0

, to generate:

21
10

,

4332
3221
3221
2110

, etc.


concatenating binary figures:
or simply populating the cells of the matrix with a ascending arithmetic series starting at 0,

initially

1

and

0

, to generate:

1110
0100

,

1111111011011100
1011101010011000
0111011001010100
0011001000010000

, etc.



The series can also be understood geometrically by visualising the superimposition of the differently scaled units which multiply to produce each subsequent generation of the matrix.

One orientation/scale of the matrix,

matrix_1b
matrix_2b
matrix_3b

superimposed over the other, at 50% opacity

matrix_1a
matrix_2a
matrix_3a

produces,

matrix_1
matrix_2
matrix_3

which, carried over to the next column at both scales,



At any one level of the matrix, each cell is multipiled by the entire matrix in order to produce the next generation of cells in that fraction of the matrix. 

Octaves

A piece based on the concepts developed in Matrix, displayed as part of the Instrumental show at the Gallery Project in Ann Arbor, MI

octaves

Detroit artist Sambuddha Saha's three-part photo print "Octaves: 2nHz, 4nHz, 8nHz" pulses with an energy that flows from the collision of math, op-art and the synaptic "a-ha!" moments that come when a complex concept like sound frequencies are rendered in visual metaphor. Deceptively simple, "Octave" is a sequence of three 2-foot-by-2-foot prints with solid dots of varying shades of gray on white. Sit with it for a while, and the idea reaches out of the static – Chris Handyside, Metro Times, April 11 2007 

Other Projects

Cult CollectionSystems / Fashion

Scout NavigatorSystems / Automotive

Coca- Cola FreestyleSystems / Food Service

Home Depot MobilitySystems / Retail

Prada Epicenter NYSystems / Retail

Taco Bell Omni-ChannelSystems / Food Service

OpenTable On-BoardingSystems / Operations

Mi Ola SurfBrand / Strategy

Smart Grid RolloutCommunications / Strategy

Cultural LootCommunications

Infinity > Infinity + 1Computational Art / Binary

MatrixComputational Art / Binary

WiresComputational Art / Binary

ShuffleComputational Art / Games

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