[ann] prime-patterns; hexagon-0.1

[Simon Strandgaard]

What is this project about?

To discover the mystery behind prime-numbers (optimistic).
I belive that the sequence of prime-numbers has to be found
within somekind of evolving pattern. This project aims to
generate a wide range of patterns. Hopefully one day,
someone will be able to extract the sequence of prime-numbers
from these patterns.


features of the hexagon-0.1 package:
Investigates an existing hexagonal-pattern for
places where the next ball can be attached.
The information it resolves are:
diameter,
distance from center to attachment-point,
number of isolated balls.
By sorting the possible attachment-points on these
properties, It can generate a wide range of cool
patterns.


homepage:
http://prime.rubyforge.org/

an example of hexagon patterns:
http://prime.rubyforge.org/hexagon1/pat1.html

download:
http://rubyforge.org/download.php/133/hexagon-0.1.tar.gz


Tell me if you find it interesting

 

[denis]

What is this project about?

To discover the mystery behind prime-numbers (optimistic).

Yes it is optimistic, but only crazy people discover interresting things

I didnt find a definition of what you call "hexagon pattern" on your site

is that a well defined mathematical object or what ?
and what is the relation with prime numbers ?

 

[Simon Strandgaard]

Yes it is optimistic, but only crazy people discover interresting things

I didnt find a definition of what you call "hexagon pattern" on your site

Yes, you are absolutly right, I have forgotton to add some text.
This was my intension to add to the 'hexagon' page. but somehow
I maneged to forget it. Sorry.

http://prime.rubyforge.org/

The algorightm for the hexagon pattern generator:

1) glue 3 balls together into a pattern.

2) attachment-places ::= walk around the current pattern
and identify possible places where a new ball can be
inserted (it must at least have 2 neighbor-balls).

3) fake an insertion of a ball for each of the
attachment-places, and measure these properties:

diameter: applying convex-hull to the pattern
and then identifying the longest distance.

distance from centrum to fake ball: pythagoras.

number of isolated balls:.

candidates4insertion ::= the above properties gets
collected into this list.

5) candidate ::= pick a candidate. In this step I try out
many different candidates. Selecting element
#0 results in what I call a 'best case' pattern.
#1 results in what I call a 'second best case' pattern.
#-1 results in a 'worst case' pattern.
You can play around with #create in this file:
http://rubyforge.org/cgi-bin/cvsweb...ntent-type=text/x-cvsweb-markup&cvsroot=prime

6) insert a ball at the candidate place

7) goto step 2.

is that a well defined mathematical object or what ?

My matematical skills isn't that good

and what is the relation with prime numbers ?

It is not yet related to prime-numbers... I havn't found
the magical sequence of patterns, yet.



BTW: How does one maximizes the number of distinct
triangles inside a hexagon grid (where the edges are
only allowed to be '1' unit long) ?