The Sierpinski triangle page to end most Sierpinski triangle pages
1–10 of 61 posts
Re: The Sierpinski triangle page to end most Sierpinski triangle pages
#2Just about ended my Chrome session, until I killed the tab.
Re: The Sierpinski triangle page to end most Sierpinski triangle pages
#3So cool. Fractals were the thing that got me into high-level math and programming, back in high school. One of these days I'm going to go re-implement a bunch of the fractal-generation algorithms.
Re: The Sierpinski triangle page to end most Sierpinski triangle pages
#4Triforce spotted :)
Nice to come across some fellow Zelda fanboys unexpectedly.
Re: The Sierpinski triangle page to end most Sierpinski triangle pages
#5That's amazing. It just goes on and on with beautiful plots. About halfway down, there's a section on understanding the Riemann sphere:
> From what I can tell, one of the settings used to deal with division by 0 is the so-called Riemann sphere, which is where we take a space shuttle and use it to fly over and drop a cow on top of a biodome, and then have the cow indiscriminately fire laser beams at the grass inside and around the biodome. That's my intuitive understanding of it anyway.
And there's even animation (with Mathematica source) for this one. However:
> (Note the cow cannot be spherical or it will roll off).
Re: The Sierpinski triangle page to end most Sierpinski triangle pages
#6[deleted]
Re: The Sierpinski triangle page to end most Sierpinski triangle pages
#7Another cool thing about the Sierpinski gasket is that it's possible to more or less do calculus on it. You can even define a Laplacian operator. There's actually a whole class of fractal-like sets on which this is possible, but SG has always been the prototypical one.
Re: The Sierpinski triangle page to end most Sierpinski triangle pages
#8That's amazing. It just goes on and on with beautiful plots. About halfway down, there's a section on understanding the Riemann sphere: > From what I can tell, one of the settings used to deal with division by 0 is the so-called Riemann sphere, which is where we take a space shuttle and use it to fly over and drop a cow on top of a biodome, and then have the cow indiscriminately fire laser beams at the grass inside a…
(I am not a mathematician) but if you want an actual explanation of the Riemann sphere, I really like the one given in "Visual Complex Analysis" by Tristan Needham. It's really very cool. Google books may have it.
This site is amazing though. It just keeps going...
Re: The Sierpinski triangle page to end most Sierpinski triangle pages
#9A few years ago, I accidentally found this way of creating a Sierpinski Gasket-like structure:
Lines "flow" from left to right (horizontally) or bottom to top (vertically), and all lines start out white. When two lines cross, they might switch color depending on which color they come across, as follows:
* white (h) + white (v) = black (h) + black (v)
* black (h) + black (v) = black (h) + black (v)
* white (h) + black (v) = white (h) + white (v)
* black (h) + white (v) = white (h) + white (v)
Re: The Sierpinski triangle page to end most Sierpinski triangle pages
#10I was thinking about Sierpinski triangles recently, and trying to relate it to the 3 4 5 triangle. The 3 side has a Sierpinski triangle, with 9 segments, equaling 3^2. The 4 side has an equivalent "Sierpinski square", with 16 segments, equaling 4^2 (basically four squares touching at the corners with an empty square space in the middle, forming a cross shape). Then I was going to show how the two shapes could be combined to equal 5^2, or come up with its own shape (a house seems best, as the regular pentagon tiles the plane so the line totals don't work out).
As of yet, fruitless. It's a cute little project that shades of the standard presentation of three squares forming a center 3 4 5 triangle, with an interesting twist.