http://www.njohnston.ca/2009/06/the-collatz-conjecture-as-a-fractal/ A blog of recreational math and quantum information theory Wed, 16 May 2012 11:07:19 +0000 hourly 1 http://wordpress.org/?v=3.3.2 http://www.njohnston.ca/2009/06/the-collatz-conjecture-as-a-fractal/#comment-2805 singularnickname Thu, 12 Apr 2012 14:46:57 +0000 http://www.nathanieljohnston.com/?p=363#comment-2805 Heh. I've just started writing my new blog about collatz problem and I came on this site by case. And I've just seen that your blog looks almost the same like mine and whats more you have writing about quite the same topics like me. Interesting correlation... Heh. I’ve just started writing my new blog about collatz problem and I came on this site by case. And I’ve just seen that your blog looks almost the same like mine and whats more you have writing about quite the same topics like me. Interesting correlation…

]]> http://www.njohnston.ca/2009/06/the-collatz-conjecture-as-a-fractal/#comment-2695 Nathan Sun, 25 Mar 2012 19:19:51 +0000 http://www.nathanieljohnston.com/?p=363#comment-2695 Great article! This morning I was thinking about whether anyone had thought about examining the Collatz conjecture with fractals and I found your blog. Keep up the good work :) Great article! This morning I was thinking about whether anyone had thought about examining the Collatz conjecture with fractals and I found your blog. Keep up the good work

]]> http://www.njohnston.ca/2009/06/the-collatz-conjecture-as-a-fractal/#comment-2146 Mario Peral Manzo Fri, 06 Jan 2012 14:37:58 +0000 http://www.nathanieljohnston.com/?p=363#comment-2146 Sending e-mail address where related article published http://hosting.udlap.mx/profesores/miguela.mendez/alephzero/archivo/historico/az60/granizo60.html Sending e-mail address where related article published
http://hosting.udlap.mx/profesores/miguela.mendez/alephzero/archivo/historico/az60/granizo60.html

]]> http://www.njohnston.ca/2009/06/the-collatz-conjecture-as-a-fractal/#comment-1151 Nathaniel Fri, 01 Jul 2011 14:11:07 +0000 http://www.nathanieljohnston.com/?p=363#comment-1151 <a href="#comment-1143" rel="nofollow">@Rammohan.R</a> - It was a while ago now, but I believe I used <a href="http://http://www.ultrafractal.com" rel="nofollow">Ultra Fractal</a>. @Rammohan.R – It was a while ago now, but I believe I used Ultra Fractal.

]]> http://www.njohnston.ca/2009/06/the-collatz-conjecture-as-a-fractal/#comment-1143 Rammohan.R Tue, 28 Jun 2011 11:09:33 +0000 http://www.nathanieljohnston.com/?p=363#comment-1143 I like to know what software you had used to generate fractal surface of f(z) and g(z )at z= one integer value. Moreover is it possible to get fractal image of 3x + 1 or 3z+1 mapping at discrete values. I like to know what software you had used to generate fractal surface of f(z) and g(z )at z= one integer value. Moreover is it possible to get fractal image of 3x + 1 or 3z+1 mapping at discrete values.

]]> http://www.njohnston.ca/2009/06/the-collatz-conjecture-as-a-fractal/#comment-1085 Collatz Conjecture and its proof @ Phi - The Mathy Mag Sat, 04 Jun 2011 07:47:30 +0000 http://www.nathanieljohnston.com/?p=363#comment-1085 [...] If we map the Col­latz conjecture’s oper­a­tion into a sin­gle func­tion, we can iter­ate that for val­ues on the com­plex plane, and obtain a frac­tal (where the black regions include num­bers whose orbit on the repeat­ing the func­tion, is bounded) — and frac­tals being the same thing we men­tioned often involve a lot of Phi! For now, I will leave you to appre­ci­ate the inter­est­ing­ness of the frac­tal, but we will cer­tainly come back to it soon! If you want to under­stand it bet­ter, you could try out your hand (or head, actu­ally) at Wikipedia, or at an analy­sis by Nathaniel John­ston. [...] [...] If we map the Col­latz conjecture’s oper­a­tion into a sin­gle func­tion, we can iter­ate that for val­ues on the com­plex plane, and obtain a frac­tal (where the black regions include num­bers whose orbit on the repeat­ing the func­tion, is bounded) — and frac­tals being the same thing we men­tioned often involve a lot of Phi! For now, I will leave you to appre­ci­ate the inter­est­ing­ness of the frac­tal, but we will cer­tainly come back to it soon! If you want to under­stand it bet­ter, you could try out your hand (or head, actu­ally) at Wikipedia, or at an analy­sis by Nathaniel John­ston. [...]

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