c = -0.624 + 0.435j.
Amplitude is in grey, phase in colour. What this shows is that each iteration is a conformal mapping. It starts from a large circle, and deforms it outside until reaching a steady state oscillation inside.
Made using Ubuntu Linux, Python, numpy, PIL, ffmpeg. There are some quality problems. I may correct it later.
ah ok I get it now. ... By: doubleOR1. on 20 Jul 11, 05:44:33 ah ok I get it now.. lol thanks. Cool? video
***correction***
... By: AkiraBergman. on 20 Jul 11, 05:41:13 ***correction***
You would hear an increasing density --->? You would hear a decreasing density.
(continued)
Now you ... By: AkiraBergman. on 19 Jul 11, 22:41:51 (continued)
Now you would hear a locally non-smooth yet globally smooth sequence of clicks, in other words the weird buzz you hear. The global smoothness is due to? the prime number theorem. The local roughness shows the semi-randomness of the primes.
Imagine all natural ... By: AkiraBergman. on 19 Jul 11, 22:38:52 Imagine all natural numbers? from 1 to infinity, on a line. Now imagine playing a click for each number in a certain frequency. You would hear a regular beat of clicks. If you increase the frequency, you would hear a smooth buzz. The sound of this buzz would depend on the spectrum and width of the click. Now, calculate n/log(n) for each number and play that instead. You would hear an increasing density. Next, remove all numbers except the primes.
well, how are the ... By: doubleOR1. on 19 Jul 11, 04:33:36 well, how are the prime numbers turned or represented by? sound?
Please read the ... By: AkiraBergman. on 18 Jul 11, 08:22:28 Please read the comments and if you have specific questions I am happy to? help.
uh. What is this? ... By: doubleOR1. on 18 Jul 11, 08:17:08 uh. What is this? I'm lost.?
Exactly.? By: yannbane. on 02 Jul 11, 13:24:21 Exactly.?
In some cases the ... By: AkiraBergman. on 26 May 11, 04:42:02 In some cases the base may be important to consider. Perhaps not here, since in the end all calculations are done in binary? anyway.
Ah, ok.? I know ... By: skatty14. on 26 May 11, 04:14:39 Ah, ok.? I know that multiplication is the same (and I suppose all math is the same) regardless of base. Prime numbers just don't seem the same in say base 2 or something. We are just all so accustomed to base 10 that others almost seem wrong? :)
There should not be ... By: AkiraBergman. on 25 May 11, 07:44:28 There should not be any difference according to the base used. To explain further, the time dimension is? the number dimension. For every prime a click is played.
Haha, this is ... By: skatty14. on 24 May 11, 21:19:15 Haha, this is awesome! This is for numbers in base 10, right? Is there much difference in the noise between this and? other bases?
fascinating? By: atree3. on 13 Mar 11, 23:20:37 fascinating?
It maybe better for ... By: AkiraBergman. on 17 Sep 10, 01:02:06 It maybe better for the child if the sound is passed through a low-pass filter, and then maybe increase the bandwidth as he/she? get used to it ;)
I'm going to? play ... By: LogicalPhallusy. on 17 Sep 10, 00:44:34 I'm going to? play this over and over loudly next to my baby's crib so he'll have an intuitive understanding of prime numbers.
Interesting ... By: AkiraBergman. on 16 Mar 10, 19:51:14 Interesting observation. Riemann Zeta function adds up? to many pi related values. This may be what you see.
do these prime have ... By: nickharvey7. on 16 Mar 10, 09:20:16 do these prime have anything to do with pi? there seems to be a curvature in the pattern that keeps? forming
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