Spiro-Fibonacci sequences

[Neil Fernandez]

In message <516653937EB0D21186930008C759B67E1405106E at ntxamos01.azit.micr
on.com>, frusso <frusso at micron.com> writes

>Neil the pictures that you obtained are very similar to those obtained by a
>cellular automata of class 3.
>Anyway very interesting data.

Hi Felice, and many thanks for pointing this out. I haven't studied
cellular automata, although I know the basic idea (as in Conway's 'Life'
and stuff :-) ).

The patterns from Differential Spiro-Fibonacci sequences may perhaps be
obtainable from a 2D CA with three cell states: 0, 1, and 'unfilled'. At
each stage, only one cell, an unfilled one, is changed. But I haven't
been able to find a way of identifying whether or not a cell is the cell
to be changed, just by looking at a finite neighbourhood that doesn't
need to increase in size as the number of filled cells increases. I
worked out the pattern by dividing the 2D lattice into eight sections,
and then changing all cells at once (apart from the first two). The part
of a cell's neighbourhood to look at depends on which of the eight
sections the cell is in. The rule details are such that there is no
circularity problem.

Best regards,

Neil

-- 
Neil Fernandez