Matrix & Octaves
2007 / Concept & Execution
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
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:
| 4 | 2 |
| 2 | 1 |
,
| 16 | 8 | 8 | 4 |
| 8 | 4 | 4 | 2 |
| 8 | 4 | 4 | 2 |
| 4 | 2 | 2 | 1 |
, etc.
adding powers of 2:
initially
| 1 |
and
| 0 |
, to generate:
| 2 | 1 |
| 1 | 0 |
,
| 4 | 3 | 3 | 2 |
| 3 | 2 | 2 | 1 |
| 3 | 2 | 2 | 1 |
| 2 | 1 | 1 | 0 |
, 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:
| 11 | 10 |
| 01 | 00 |
,
| 1111 | 1110 | 1101 | 1100 |
| 1011 | 1010 | 1001 | 1000 |
| 0111 | 0110 | 0101 | 0100 |
| 0011 | 0010 | 0001 | 0000 |
, 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,
superimposed over the other, at 50% opacity
produces,
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
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