Category Archives: Number Systems

DIGITAL #ICHING: new #Patterns, #Designs and a new #Science thanks to Octal Numbers

This Gnostic Book of Changes quotes Terence McKenna:

The I Ching is no magic; it is a science we don’t understand.

t-shirtThe science that I am offering, comprises a new understanding of

The use of octal numbers has allowed me to find ‘stable’ hexagrams, i.e. those with dual octal digits: the values 00, 11, 22, 33, 44, 55, 66, 77. 

In digital designs, they can be represented from four ‘view points’ or ‘cornerstones’:

When used for divination, two hexagrams are used: one to represent the Here and Now and a second one that the current situation changes into, based on those lines that change when we make our conventional or binary divination.

The position of two hexagrams within a set of hexagrams and eight different sets adds new scope for interpretation:

1. Which ‘quadrant’ or ‘directional context’ of change do our two hexagrams occupy? That depends on the ‘intensity’ of change, as indicated by the ‘stability’ of the two hexagrams:

  • Stable UnstableTop Right, if both are stable;
  • Top Left, if the first is stable and the second one unstable;
  • Bottom Left, if both are unstable;
  • Bottom Right, if the first is unstable and the second one is stable.

P F U CThe meaning of the quadrant position is explained also under polarities:

  • the Left is the Past and the Right is the Future
  • the Top is Consciousness and the Bottom is Unconsciousness.

2. Which ‘plane’ are we moving from and to:

  •  4 Quadrants 00 7700 or Dark (Earth, night) to 77 or Light (Heaven, day):
  • becoming conscious of ourselves and our world – as on the left – if the first hexagram is < or smaller than the second one;
  • here the four ‘quadrants’ are home to complete sets of hexagrams – showing fourfold symmetry – both visually and numerically.

It is this combination of visual beauty and numerical accuracy that adds new value to this ancient wisdom.

Or are we moving

4 Quadrants 77 00

  • 77 or Light (Heaven) to 00 Dark (Earth):
  • becoming inspired by the Universe – as on the left – if the first hexagram is > or greater than the second one.

3. How do we interpret the comparisons of visual positions and numerical values of two hexagrams?

  • Stable hexagrams in diagonals illustrate directions of change: between Light (day) and Dark (night).
  • Quadrants of single sets of hexagrams bridge polarities of time: past and future as well as awareness: unconscious and consciousness.
  • Planes of four sets of hexagrams bridge polarities of space: Heaven and Earth as boundaries for humans: inspiration and manifestation.

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DIGITAL #ICHING Hexagrams in new Visual Order thanks to Octal Numbers

Matrix with Grid and NumbersRow 0 contains hexagrams 00, 0107.

Row 1 contains hexagrams with octal values 10, 1117.

Row 7 contains hexagrams 70, 7177.

And so it goes:

a new visual order thanks to a new numerical order!

1 00 77Above all, marvel at the beauty of the visual and numerical symmetries!

These are the first images I produced with GIMP.

I can’t use more than 3 colours if I also want to use the visual diagrams as digital designs on t-shirts and other accessories.

Let’s see where the digital paintbrush will lead me…

In the next collection of diagrams you will notice the symmetry created by organising the hexagrams in four different ways:

  • from four ‘corner stones’ or ‘zero point’ positions.

Thus they form a new kind of ‘visual ensemble’:

Light (heaven) at the centre radiates towards Dark (earth) on the outskirts.

And now in reverse order, with earth at the centre and light at the periphery:

Or with the highlights of colour:

1. from 00 to 77, i.e. Earth to Heaven, starting at four different corner points:

2. from 77 to 00, i.e. Light or Heaven to Darkness or Earth:

More on:

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DIGITAL #ICHING: Octal Numbers as new Ordering Principle & 8 as Chinese lucky number

I wish I could remember what made me

Funky Facts about 8

think of what now is so obvious: the use of octal numbers to re-order the hexagrams 1 to 64 (base 10) from 00 to 77 (base 8), leading to remarkable visual effects.

So I used

  • trigrams numbered from 0 to 7
  • and hexagrams counted from 1 to 64
  • to renumber them from 00 to 77

and produced a lot of

Hence I was amused to discover that for the Chinese, the New Year is the Year of the Sheep, starting 19 February, with the number 8, considered to be the luckiest number, being ubiquitous, as said on this site.

I Ching hexagrams 00 to 77 with: left the firs...

I Ching hexagrams 00 to 77 with: left the first octal digit for the lower trigram under the second octal digit (upper trigram) (Photo credit: Wikipedia)