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comp.lang.ruby

[ann] prime-patterns; hexagon-0.1

Simon Strandgaard

10/4/2003 12:34:00 PM

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.ruby...

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

download:
http://rubyforge.org/download.php/133/hexagon-...


Tell me if you find it interesting :-)

--
Simon Strandgaard
2 Answers

dmertz

10/7/2003 2:02:00 PM

0

Simon Strandgaard <qj5nd7l02@sneakemail.com> wrote in message news:<pan.2003.10.04.12.34.04.500993@sneakemail.com>...
> 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

10/7/2003 4:36:00 PM

0

On Tue, 07 Oct 2003 08:02:00 -0700, denis wrote:

> Simon Strandgaard <qj5nd7l02@sneakemail.com> wrote in message news:<pan.2003.10.04.12.34.04.500993@sneakemail.com>...
>> 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

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.ruby...

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.cgi/projects/hexagon1/build_web_site.rb?rev=1.1&content-type=text/x-cvsweb-markup&cvs...

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) ?

--
Simon Strandgaard