lucas cycle



Lucas numbers: the exponential expression of Phi

modulo 9 mental objects exploring the patterns produced using

mod9 Pisano Period 24


graphics on canvas

30ins x 30ins

3-6-9-0 framework

lucas cycle construct

lucas cycle A+B

master lucas cycle

master lucas cycle 3-6-9-0 framework composite lucas cycle lucas cycle black pisanoperiods

Pisano Periods:

Repeating cycles of modulo values derived from the Lucas series.

selection of working data:

Modulo 9 (mod9) Pisano Period of 24

Master Lucas Cycle construction - breakdown of values.

[Notice how the Lucas series is developed out of the Fibonacci series by alternate addition of Fibonacci values]

[Notice also the framework nature of 3-6-9-0 values, in red]

basic table

Processing in Modulo 9 (mod9) is commonly termed transposing to the Vedic Digital Root. It is used in Numerology.

'Casting out the Nines' is a technique introduced to Europe at the same time as the Fibonacci Series. This technique can only refer to Modulo 9 processing where 9 is equivalent to 0.


Below I tabulate all but one of the possible Modulo 9 additive series.

(I ignore the 0-9 Series since all values are 9 aka 0).

Notice a Reciprocal / Reflective pattern.

Column 1 = Series 1-8 is the Fibonacci Series (Yellow - Pink).


The Lucas series pattern of Modulo 9 digits is found in the

Column 2 = Series 2-7 (Beige - Pale Green) &

Column 7 = Series 7-2 (Pale Green - Beige),

However there is a precise order of unalterable values in Lucas which exempts it from this table. Lucas values are locked in to both Fibonacci values & exponential Phi values.

All one can say is that the Lucas Series is of a class (2-7), (7-2) additive series.