Discussion in 'Physics & Math' started by James R, Oct 4, 2018.

1. ### James RJust this guy, you know?Staff Member

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This is a thread to post interesting and/or fun stuff about the mathematical constant pi ($\pi$).

To get the ball rolling, here's an image of the first 786,432 digits of $\pi$ as a 1024x768 image. Each individual pixel is one digit in the decimal expansion, with the digits 0-9 each having a different colour.

Last edited: Oct 4, 2018

3. ### James RJust this guy, you know?Staff Member

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32,166
Here's another visualisation. This time, we write pi in base 4, then use the digits to follow a path in 2-D space. Here 0 is north, 1 is south, 2 is east and 3 is west.

This was generated by Francisco Aragón. Sourced from an article The Guardian, here (14 March 2014).

The image is generated using the first 100 billion digits (presumably base 4 digits) of pi.

5. ### Quantum QuackLife's a tease...Valued Senior Member

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18,915
excellent... now can you do the same with random numbers using a random number generator?
so we can compare..

(if you don't have the software maybe another member might be able to help out.)

7. ### DaveC426913Valued Senior Member

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I wonder what the next number smaller than 786,432 that is the sum of two primes is.

Then you could redo the matrix with those two primes as lengths of the sides.

I guess won;t get far - it's a Sisyphean task, since you could choose any number that's the sum of two primes and look at the result.

8. ### Neddy BateValued Senior Member

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1,761

Starting from the upper left corner, going from left to right:
magenta = 3
white = "."
cyan = 1
green = 4
cyan = 1
orange = 5
black = 9
blue = 2
red = 6
orange = 5
magenta = 3
orange = 5
gray = 8
black = 9
yellow = 7
black = 9

I guess white serves as both zero and the decimal point.

Last edited: Oct 5, 2018
9. ### DaveC426913Valued Senior Member

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Am I imagining things, or is there a hint of pattern in that noise?

10. ### Neddy BateValued Senior Member

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1,761
You are imagining things.

First of all, each horizontal line being 1024 pixels is arbitrary. Choose a different number, and you will get a different pattern.

Also, any random sequence of those same 10 colors, would look much like that, in any arrangement.

11. ### Quantum QuackLife's a tease...Valued Senior Member

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18,915
If the picture generated was circular? Say starting center outwards?
(Example: the center pixel would be the leading number 3.)

12. ### DaveC426913Valued Senior Member

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Nobody gets me.

Look again, from a distance...

13. ### Write4UValued Senior Member

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I see a fractal network, darker colored connecting lines all throughout the picture.
If you unfocus your eyes it becomes clearly visble.

14. ### Michael 345New year. PRESENT is 69 years oldValued Senior Member

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I got with unfocused eyes
• Circle on the left edges touching left edge and top and bottom
• Orchid
• Spacesuit feet bottom left corner leaning about 45°
What was I supposed to see?

Face of jesus?

NAA I only see him on burnt toast

15. ### TheFroggerValued Senior Member

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Shouldn't that be burnt pi?

16. ### Michael 345New year. PRESENT is 69 years oldValued Senior Member

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Don't burn my pi's

Six minutes in microwave with a cup full of water to keep the pi pastry soft

Toast I have baby jesus and face of jesus

Still waiting on the cross carrying Jesus

Unfortunately the toastjesushere.com closed down

17. ### DaveC426913Valued Senior Member

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Oh my God people. Your eyes are worse then mine.

18. ### TiassaLet us not launch the boat ...Staff Member

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I'm just wondering if anyone bothered to view the picture at full size.

Because when you scroll to examine another part of the noise, it shows during the redraw.

On an i5 Dell laptop running Linux.

Results may vary.

(It was actually a pretty good joke, all things considered, a fitting tribute.)

19. ### Neddy BateValued Senior Member

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Pull the other one.

20. ### TheFroggerValued Senior Member

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The meaning of life, the universe and everything. Didn't they build a giant computer to solve such a question, and they called the computer Earth??

21. ### arfa branecall me arfValued Senior Member

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6,148
How noisy is the image of pi? Is it possible to consider a 2-dimensional array as a colouring of pi; what that means abstractly is we take the digits of pi to the nodes of a graph and colour the nodes depending on the value or weight of each digit.

So what colour is the first say, quadrillion digits? It will look like a single colour, beige perhaps, from a sufficient distance. Up close (at 1024x768 resolution the nodes are visible) you can see 'different' colours. There's that word again.

I notice changing the resolution (ctrl+) on my PC introduces a square-ish pattern to the image.
Has anyone else noticed this?
The square pattern I see gets smaller as the text size increases (using Ctrl+), I'm guessing it's an artefact of the rendering algorithm.

Last edited: Oct 7, 2018
22. ### Quantum QuackLife's a tease...Valued Senior Member

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18,915
We did this one here ( in collaboration) probably over 10 years ago:
I can't recall the specifics of how.