What is this mathematically ?

[eighth man]

I wrote a small program that generates alot of

regularity:

 

$pattern=

"#################################################################################################";

$r=1;

 

for(0..366000)

{

$x=1/($r**2);

$r=$r+0.01;

@t=split/\./,$x;

$t[1]=~m/^..(.)..(.)../; $p=$2.$1;

print $p.' '.substr($pattern,0,$p)."\n"

}

 

 

You can see the result by entering c:>perl this.pl > rw

 

and browsing through rw with word at 10% size (choose normal view)

 

Is this a fractal or chaos or something unknown ? it is the combination

of a formula and a simple logical operation that extracts a couple of

digits of the precision and graphs numbers out of them.

 

The / .../ matches the digits and $1 and $2 identifies which.

 

Any clues if these things are already known ?

 

Thanks eighth man

[Dave]

For those of use not familiar with perl, can you explain your algorithm a bit more? I think I know what it's doing, but I'm not 100% sure.

[eighth man]

Ok. The only thing really hard is the split and pattern matching

thing. the @t=split/\./,$x; is splitting the number $x between it's

whole number place and decimal place putting it in 2 slots of the

array @t (which in perl can also be written $t[) so for $x=3.234

$t[0] is equal to 3 and $t[1] is equal to 234. Next you extract

some character from the pattern $x[1] according to position

with the syntax $t[1]=~m/....../; each dot is the corresponding

character the first dot is 2 the second is 3 etc. Put (.) to identify the

character and it is $1 or $2 according to if it is the first or second

paranthesese. so if if $t[1] is 234 then $t[1]=~m/(.).(.)/ would make $1

equal to 2 and $2 equal to 4.

 

Sorry I didn't think it was too complicated but maybe I use perl too much..

 

It could be done in other languages but this is the fastest way. I find

the resulting drawing which I scroll with word really strange! It has

alot of regularity but it doesn't seem to come from nowhere. I don't

know if this is already known mathematically or if it is a new discovery.