Is this not just generating a random walk from a pseudorandom number generator.
Footsteps of pi
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Re: Footsteps of pi
#12I wonder if the path stays consistent in other (maybe very high) number bases, or if that general path is random and unique to base-10
The path will look entirely different depending on the base you choose, but all paths for all bases should look roughly equally "random" because it's widely believed that π is a normal number:
Re: Footsteps of pi
#13> I originally created this image in early 2020 to impress and woo my now-girlfriend, who I adore. Dating gurus hate him for this one weird trick.
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Re: Footsteps of pi
#14Is this not just generating a random walk from a pseudorandom number generator.
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Re: Footsteps of pi
#15I 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
Re: Footsteps of pi
#16See also "π plays Pokemon Sapphire", currently at 372 24-hour segments, and still stuck in the starter town (with a level 76 Sceptile):
Re: Footsteps of pi
#17I 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.
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
Re: Footsteps of pi
#18Also 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
Re: Footsteps of pi
#19Also 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?
Re: Footsteps of pi
#20Is this not just generating a random walk from a pseudorandom number generator.
It is not a traditional uniform random walk because the next movement is based on the previous movement, but it is a random walk. It is a pseudo-random number generator of sorts, and has properties very close to a uniform pseudo-random number generator because PI is likely normal.