31–38 of 38 posts
> The colors are arbitrary, and have no deeper meaning I thought that colouring the pattern by the instantaneous velocity of the ball would be an obvious improvement and might uncover further structure.
> The colors are arbitrary, and have no deeper meaning I thought that colouring the pattern by the instantaneous velocity of the ball would be an obvious improvement and might uncover further structure.
There's no structure here- it's a random walk.
Earlier quoted context omitted.
Well some numbers expose patterns when written as a continued fraction. In particular e becomes pretty regular. You can modify the continued fraction slightly to make pi regular as well, but the normal continued fraction sequence doesn't give much of an insight. Other than the fact that 3 + 1/(7 + 1/16)) is a damn good approximation (7 digits, pretty good for something that can be written using only 4 digits total: […
Phi/golden ratio also has a cool continued fraction sequence...it's only 1's all the way down
I always wondered if some hidden pattern would be exposed when visualising numbers in unconventional ways in numbers with no known pattern such as Pi or prime numbers. A sort of multi-dimensional rendering that suddenly reveals a hidden pattern.
One example is Ulam spiral: https://en.wikipedia.org/wiki/Ulam_spiral
Also If you do this for the Square Roots of the integers you can see every integer root is special and has it's own kind of shape. And the Squares are also very interesting in that they have no shape in this viewpoint. Just a dot. So you go from infinitesimal chaotic walk patterns to a single dot depending on if the integer is a square or not. maybe there could be a database, online encyclopedia of random-walks
I would think the squares are a line, not a dot?
> The colors are arbitrary, and have no deeper meaning I thought that colouring the pattern by the instantaneous velocity of the ball would be an obvious improvement and might uncover further structure.
There's no structure here- it's a random walk.
Earlier quoted context omitted.
There's no structure here- it's a random walk.
pi is normal, similar to but not random.
Closest I found was https://en.wikipedia.org/wiki/Normal_number, but this seems to mean that no matter what base you choose the digits are uniformly distributed. Meaning, yes, it's random.
Although, this SE thread: https://math.stackexchange.com/questions/51829/distribution-... seems to indicate that pi is not proven to be normal
Earlier quoted context omitted.
I would think the squares are a line, not a dot?
well depends on how you interpret, could take '0' to mean 'stay where you are' or you could mean it 'go west' or whatever. but yes.