POV-Ray : Newsgroups : povray.binaries.images : Ulam Spiral fun Server Time
29 Sep 2022 17:16:23 EDT (-0400)
  Ulam Spiral fun (Message 1 to 10 of 28)  
Goto Latest 10 Messages Next 10 Messages >>>
From: Robert McGregor
Subject: Ulam Spiral fun
Date: 23 Feb 2022 16:55:00
Message: <web.6216acf8b272bd4f87570eabd4644d08@news.povray.org>
A simple Ulam spiral displaying the locations of the first 2088 prime numbers (2
- 18229) with cylinders marking out the spiral path itself.


Post a reply to this message


Attachments:
Download 'rwmulamspiral_1080x1080.jpg' (1177 KB)

Preview of image 'rwmulamspiral_1080x1080.jpg'
rwmulamspiral_1080x1080.jpg


 

From: Robert McGregor
Subject: Re: Ulam Spiral fun
Date: 23 Feb 2022 17:00:00
Message: <web.6216ad9b8a87000087570eabd4644d08@news.povray.org>
Here's a version that's four times larger than the previous post.


Post a reply to this message


Attachments:
Download 'rwmulamspiral_2096x2096.jpg' (3395 KB)

Preview of image 'rwmulamspiral_2096x2096.jpg'
rwmulamspiral_2096x2096.jpg


 

From: David Buck
Subject: Re: Ulam Spiral fun
Date: 23 Feb 2022 21:52:46
Message: <6216f2fe$1@news.povray.org>
This visualization is mesmerizing.  It shows that the primes aren't 
completely random but they also aren't predictable.  It really makes you 
think about the nature of primeness.

Thanks for sharing.
David Buck


On 2022-02-23 4:54 p.m., Robert McGregor wrote:
> A simple Ulam spiral displaying the locations of the first 2088 prime numbers (2
> - 18229) with cylinders marking out the spiral path itself.


Post a reply to this message

From: David Buck
Subject: Re: Ulam Spiral fun
Date: 23 Feb 2022 21:54:25
Message: <6216f361$1@news.povray.org>
BTW, is there any reason some of the spheres are green and others are blue?

Thanks,
David Buck

On 2022-02-23 4:56 p.m., Robert McGregor wrote:
> Here's a version that's four times larger than the previous post.


Post a reply to this message

From: Robert McGregor
Subject: Re: Ulam Spiral fun
Date: 24 Feb 2022 12:00:00
Message: <web.6217b8c58a87000087570eabd4644d08@news.povray.org>
David Buck <dav### [at] simberoncom> wrote:
> This visualization is mesmerizing.  It shows that the primes aren't
> completely random but they also aren't predictable.  It really makes you
> think about the nature of primeness.
>
> Thanks for sharing.

Thanks David!

David Buck <dav### [at] simberoncom> wrote:
> BTW, is there any reason some of the spheres are green and others are blue?

No reason, they were all blue at first. Just for variation I added some random
green/blue coloration to each sphere:

   pigment { rgb <0, RRand(0.2, 0.5, R), RRand(0.25, 0.9, R)> }


Cheers,
Rob


Post a reply to this message

From: Paolo Gibellini
Subject: Re: Ulam Spiral fun
Date: 24 Feb 2022 13:50:00
Message: <6217d358@news.povray.org>
Il 23/02/2022 22:54, Robert McGregor ha scritto:
 > A simple Ulam spiral displaying the locations of the first 2088 prime 
numbers (2
 > - 18229) with cylinders marking out the spiral path itself.
Like a fascinating web with unique raindrops...
Paolo


Post a reply to this message

From: Thomas de Groot
Subject: Re: Ulam Spiral fun
Date: 25 Feb 2022 02:15:17
Message: <62188205$1@news.povray.org>
Op 24/02/2022 om 17:57 schreef Robert McGregor:
> David Buck <dav### [at] simberoncom> wrote:
>> This visualization is mesmerizing.  It shows that the primes aren't
>> completely random but they also aren't predictable.  It really makes you
>> think about the nature of primeness.
>>
>> Thanks for sharing.
> 
> Thanks David!
> 
> David Buck <dav### [at] simberoncom> wrote:
>> BTW, is there any reason some of the spheres are green and others are blue?
> 
> No reason, they were all blue at first. Just for variation I added some random
> green/blue coloration to each sphere:
> 
>     pigment { rgb <0, RRand(0.2, 0.5, R), RRand(0.25, 0.9, R)> }
> 
> 
> Cheers,
> Rob
> 
> 

Mesmerizing indeed. And an excellent way to show this. First time I 
heard about an ulam spiral...

-- 
Thomas


Post a reply to this message

From: jr
Subject: Re: Ulam Spiral fun
Date: 27 Feb 2022 05:40:00
Message: <web.621b54648a870000ed36e5cb6cde94f1@news.povray.org>
hi,

Thomas de Groot <tho### [at] degrootorg> wrote:
> Op 24/02/2022 om 17:57 schreef Robert McGregor:
> > A simple Ulam spiral displaying the locations of the first 2088 prime numbers
>
> ... First time I heard about an ulam spiral...

same here.  v pleasing, visually.  the Wikipedia page shows that other
arrangements are .. permissible.  attached shows primes marked on a Hilbert
Curve (sphere_sweep, 4096 points), more "patterns".  (I wonder how much of those
"patterns" is just the result of a desire to see patterns.  :-))


regards, jr.


Post a reply to this message


Attachments:
Download 'h12.png' (220 KB)

Preview of image 'h12.png'
h12.png


 

From: Kenneth
Subject: Re: Ulam Spiral fun
Date: 27 Feb 2022 11:20:00
Message: <web.621ba3b08a8700004cef624e6e066e29@news.povray.org>
David Buck <dav### [at] simberoncom> wrote:
> This visualization is mesmerizing.  It shows that the primes aren't
> completely random but they also aren't predictable.  It really makes you
> think about the nature of primeness.
>

Indeed. This is very intriguing. Your curve and JR's Hilbert example make me
wonder if there is some other kind of spiral (or more complex multi-dimensional
shape??) that would show an even clearer visual pattern to the primes. I kind of
sense that there may be something 'deeper' going on here, yet to be discovered.


Post a reply to this message

From: Alain Martel
Subject: Re: Ulam Spiral fun
Date: 27 Feb 2022 11:46:32
Message: <621baae8$1@news.povray.org>
Le 2022-02-27 à 05:37, jr a écrit :
> hi,
> 
> Thomas de Groot <tho### [at] degrootorg> wrote:
>> Op 24/02/2022 om 17:57 schreef Robert McGregor:
>>> A simple Ulam spiral displaying the locations of the first 2088 prime numbers
>>
>> ... First time I heard about an ulam spiral...
> 
> same here.  v pleasing, visually.  the Wikipedia page shows that other
> arrangements are .. permissible.  attached shows primes marked on a Hilbert
> Curve (sphere_sweep, 4096 points), more "patterns".  (I wonder how much of those
> "patterns" is just the result of a desire to see patterns.  :-))
> 
> 
> regards, jr.

Our brains are extremely good at finding patterns. Even TO good at it. 
It can, and do, find patterns even in places where there are no patterns 
at all.


Post a reply to this message

Goto Latest 10 Messages Next 10 Messages >>>

Copyright 2003-2021 Persistence of Vision Raytracer Pty. Ltd.