So, I've been thinking about pi lately, and wondering if there could be a pattern to the seemingly random sequence of digits within it. Then I thought of something else that goes on and on without repeating:
So, I thought, could a fractal number go on and on without repeating?
I made a quick program in C++ to find out for sure, and it looks like one can.
The algorithm goes like this:
| Code: |
a = 0
b = 0
c =0
d =0
e =0
>>repeat from here<<
1:
a ++
e ++
output & test for repeat of first "00000"
2:
a ++
c ++
e ++
output & test for repeat of first "00000"
3:
a ++
b ++
c ++
d ++
e ++
output & test for repeat of first "00000"
>>repeat<<
|
This creates a sequence of numbers that progresses like this:
00000
10001
20102
31213...
When it is all run into one long string, it looks random, but actually is not. The first sequence does show up occasionally, as it also would in a random number, but the numbers following it are never the same as the numbers following the first group of five.
What I was wondering is, could pi also have a pattern like this within it, and if it did, would it be possible to find it? Err...what has that rather simple program got to do with fractals? It seems to me that you are simple adding, in a deterministic fashion, to the digits of a 5 digit string. That's nothing to do with fractals and certainly nothing to do with pi.
If you want to code a nice fractal then try this:
1 Draw any triangle
2 Select a point at random within the triangle
3 Plot the point
4 Select one of the vertices of the triangle at random
5 Move halfway from where you are, to that vertex
6 goto 3
Now that WILL produce a fractal which should astonish (though it will still be nothing to do with pi which is not fractal).
True, my program there is too simple, but I was trying to make a string of digits that made a fractal-like pattern. (Perhaps the original version where digits would restart at 0 after 9 instead of 10 after 9 would have been better...) I was having trouble trying to apply a fractal pattern to a sequence of numbers.
No. You have missed the whole point of fractals.
Firstly a fractal is a geometric shape, not just a number series.
Secondly a fractal is self-similar at any magnification (ie you zoom in and see the same patterns repeating).
Thirdly it can be defined by a simple recursive procedure.
You have got number 3 but ignored the first 2.
Perhaps instead of fractal-like (self-repeating) you mean something with a pattern?
According to good ol' Wikipedia, "Despite much analytical work, and supercomputer calculations that have determined over 1 trillion digits of π, no simple pattern in the digits has ever been found."
| nilsmo wrote: |
| no simple pattern |
I guess what I mean is that it may be a complex pattern, with successive digits depending on the values of previous digits.Well it would be extremely amazing if you found one, since no patterns have been found apparently.
^Yes, actually finding a complex pattern is easier said than done. It may be impossible with today's technology to do so. Computers can only try by trial and error so far, and that could take forever because there are so many possible patterns, and if there is a pattern, it is apparently too complex to be apparent to human minds...
Perhaps if we ever have a true AI, it could do it?
Well, if you want to look for patterns in pi then try :
http://www.angio.net/pi/piquery The digits of pi may be taken to obtain a fractal geometric shape. It seems an interesting approaching.
| falacal wrote: |
| The digits of pi may be taken to obtain a fractal geometric shape. It seems an interesting approaching. |
No, as already explained in some detail - it is not an interesting approach because it doesn't work.Isn't pi the sum of the infinite series:
4(1/1-1/3+1/5-1/7+1/9-1/11+1/13-1/15+......)
Isn't this the best approach to compute irrational numbers?
Irrational numbers like square roots can be expressed as continued fractions, right?
| _AVG_ wrote: |
Isn't pi the sum of the infinite series:
4(1/1-1/3+1/5-1/7+1/9-1/11+1/13-1/15+......)
Isn't this the best approach to compute irrational numbers?
Irrational numbers like square roots can be expressed as continued fractions, right? |
But it's not a pattern of digits ie. you cannot determine certain next number of digits in pi, knowing the previous ones, using this formula.I like pi... everyone loves pi 
Pi is an irrational number, not a fractal.
| Dennise wrote: |
| Pi is an irrational number, not a fractal. |
Very good. Now, prove it!
