View Full Version : interesting patterns of pi and e

malaidas

2015-Mar-15, 02:58 PM

http://cristian-vasile.fineartamerica.com

I just came across this and have a quick question for maths boffins. The Similarities between the 2 patterns is stark, particularly the empty region in the middle is there a good known reason for this?

Squink

2015-Mar-15, 03:41 PM

Since pi is infinite, do its digits contain all finite sequences of numbers? (http://www.askamathematician.com/2009/11/since-pi-is-infinite-can-i-draw-any-random-number-sequence-and-be-certain-that-it-exists-somewhere-in-the-digits-of-pi/)

Suspicions are leaning towards yes.

Patterns being substrings, that property should cause your plots to change shape as you move further rightward from the decimal point.

Shaula

2015-Mar-15, 04:18 PM

The reason for the hole in the middle is because he put it there, it is encoded in the rules for drawing the paths. The similarity with other numbers is because of the way the paths are drawn. Any other number with a roughly uniform probability of each digit (and combination of digits) appearing would appear the same. Differences would only show up if one or more numbers or number sequences was repeated abnormally often in the series.

grapes

2015-Mar-15, 04:19 PM

http://cristian-vasile.fineartamerica.com

I just came across this and have a quick question for maths boffins. The Similarities between the 2 patterns is stark, particularly the empty region in the middle is there a good known reason for this?

Hard to tell, I can't determine exactly what algorithm was used to make the prints. There's a comment that seems to know:

Re : William Cowan "OK, so how is it determined where in the span of a number will the line go. A set number is a point not a segment or a line so this representation, no matter how interesting it may be, is flawed and inaccurate" The progression along the span of the number follows the digit sequence progression from 0 to 10,000. From inspection of digit #1 we see this rule as following a clockwise progression along the bar, so the earliest digits in the sequence will be most-clockwise on the span and most-anticlockwise will be in the last 10,000'th digits. It looks as though the path taken as the line progresses from one digit to the next follows rules that are chosen to form a pleasant pattern with 5 ranges of digits following different sets of rules. It's clearly a work of art with little mathematical value as such and I think "flawed and inaccurate" is probably stretching the intent of the artist to breaking point - if you chose a 10,000 digit random sequence you'd find the same general pattern essentially indistinguishable without detailed inspection. Nevertheless, a beautiful

I tend to think the same, that the algorithm is such that no matter what the sequence, there will be no paths that cross the middle. Looks that way.

NEOWatcher

2015-Mar-15, 05:10 PM

The reason for the hole in the middle is because he put it there, it is encoded in the rules for drawing the paths.

I agree; It looks like he intentionally picked diameter ratios that will make pretty pictures. In addition to making arcs that don't extend past the middle, they are also particular ratios that will converge to a pattern.

It's also similar to drawings I made as a kid with a spirograph. Most had holes in the middle depending on which circles and holes you chose.

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