"PM 2Ring" <nomail@nomail> wrote:
> "Janet" <par### [at] attnet> wrote:
> > "PM 2Ring" <nomail@nomail> wrote:
> > > Play with the code. Make all the triangles different colours so you can see
> > > whats going on. Do scenes with low recursion depth to see how the triangles
> > >
> > > Thanks. That one did require a bid of hard thinking to combine the two, but
> > > I think my solution is elegant.
>
> Um, that should say "a bit of hard thinking". :)
It took me three and a half hours to realize you spelled "bit" wrong.
I'll bet you're not in sales.
> >
> > I did play. Messed with a bunch of the variables. Messed with the angles
> > too, not so hot when you change them. :)
>
> I bet!
giggle
>
> > Thanks for the link. I was looking
> > at a bunch of Penrose stuff and Phi stuff a while back. Played around with
> > equiangular spirals too,
>
> I did an equiangular spiral for my introductory RSOCP post:
>
> //Pickover shell
> #macro Shell(N,A,B,C,K)
>   #local D=(11/3-A)/N; #local I=1;
>   //union{
>   merge{
>     #while(I<N)
>       #local T=I/N; #local R=B*exp(A*K);
>       sphere{
>         R*<1,0,C/B>,R rotate z*A*360
>         pigment{rgb<T, .6, 1-T*T>}
>         finish{reflection{0,1} phong .7}
>       }
>       #local I=I+1; #local A=A+D;
>     #end
>     rotate x*30 translate <1,5,-2.5>
>   }
> #end
It took me 5 minutes to find out what RSOCP was (crap, I've broken another
rule). I even saw your image in my "quest". Its excellent. I like the
colour change a lot. Actually, you're my favourite poster, seriously!!
I feel like a fookin' dope compared to the geniuses that post in the POV
Newsgroups, but that's why its fascinating.
> >see ==> http://www.deviantart.com/view/29573733/
>
> Interesting, but I agree with one of the comments that it's slightly creepy.
> Speaking of which, do you know about Alexander's Horned Sphere"? It's been
> called the ugliest object in mathematics.
Ugly math object? I will look it up right now! Cheers!

Post a reply to this message

"Janet" <par### [at] attnet> wrote:
> "PM 2Ring" <nomail@nomail> wrote:
> > Um, that should say "a bit of hard thinking". :)
> It took me three and a half hours to realize you spelled "bit" wrong.

Sorry, I had a cold. :)

> I'll bet you're not in sales.

Actually, I am in sales, kind of. I work in a call centre, taking orders for
disposable contact lenses from optometrists & their staff, but I don't
really do any actual selling or marketing.

> It took me 5 minutes to find out what RSOCP was (crap, I've broken another
> rule).

Don't worry, it's more like a tradition than a rule... but if you want
respect around here, you've gotta do one. :)

> I even saw your image in my "quest". Its excellent. I like the
> colour change a lot.

Yes, I was very happy to stumble onto that colour combo. I like playing with
colour spaces, but the best software I have for this is all on my Amiga.

> Actually, you're my favourite poster, seriously!!

Thanks! Flattery *will* get you everywhere, young lady. :)

> I feel like a fookin' dope compared to the geniuses that post in the POV
> Newsgroups, but that's why its fascinating.

Hey, compared to most of the population, anyone who can handle maths & 3D
geometry well enough to use POV is a genius. :) Besides, there has to be
some payoff for being a maths nerd. :)

> > >see ==> http://www.deviantart.com/view/29573733/
> >
> > Interesting, but I agree with one of the comments that it's slightly creepy.
> > Speaking of which, do you know about Alexander's Horned Sphere"? It's been
> > called the ugliest object in mathematics.
> Ugly math object? I will look it up right now! Cheers!

I've got a few pics of Alexander's Horned Sphere (AHS) on the Amiga, done
using an old version of POV. I'll get around to updating the eventually. In
the mean time, here's a couple on the net:

http://www.win.tue.nl/~aeb/at/hornedsphere.jpg

http://cs.stmarys.ca/~dawson/alexander.jpg

and of course

http://mathworld.wolfram.com/AlexandersHornedSphere.html

Although the AHS is topologically equivalent to a sphere, it behaves a bit
like a torus. If you tie a ribbon around it, you can't slip the ribbon off
in a finite number of steps, due to the infinite interlocking.

Alexander's Horned Sphere was discovered in the early years of the 20th
century. Back then, the fractals that had been discovered were considered
abnormal and pathological, so I guess that's why the AHS was called ugly.
Of course, all that changed with the work of Mandelbrot, et al.

Post a reply to this message

"PM 2Ring" <nomail@nomail> wrote:
> Sorry, I had a cold. :)
Ha ha!!
> Don't worry, it's more like a tradition than a rule... but if you want
> respect around here, you've gotta do one. :)
I see, maybe I should do one, if I think of something good for it.
> Although the AHS is topologically equivalent to a sphere, it behaves a bit
> like a torus. If you tie a ribbon around it, you can't slip the ribbon off
> in a finite number of steps, due to the infinite interlocking.
Sounds frustrating. :)
> Alexander's Horned Sphere was discovered in the early years of the 20th
> century. Back then, the fractals that had been discovered were considered
> abnormal and pathological, so I guess that's why the AHS was called ugly.
> Of course, all that changed with the work of Mandelbrot, et al.
"abnormal and pathological" fractals - too funny. Thanks for the pictures.

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