# Explain fractal geometry like I'm an idiot **URL:** \ **Category:** Factual Questions\ **Created:** [November 4, 2008, 2:52pm UTC](https://boards.straightdope.com/t/explain-fractal-geometry-like-im-an-idiot/471052 "2008-11-04T14:52:23Z")\ **Posts on this page:** 5\ **Page:** 4
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [November 10, 2008, 8:03pm UTC](https://boards.straightdope.com/t/explain-fractal-geometry-like-im-an-idiot/471052/61 "2008-11-10T20:03:32Z")
> [@Chronos](#): > > I spent a few minutes looking for pictures, myself, before posting that. Unfortunately the only hits I found were in journals that most folks here won’t be able to access. Fortunately the author of several of those papers is one of the professors here, so I might be able to get something from him. Are you referring to this paper? “Fractal basins and chaotic trajectories in multi-black-hole spacetimes” (Phys. Rev. D 50, R618). If so, those without a subscription to the Physical Review can view the preprint on arXiv: Follow the link for the PDF from [this page](http://arxiv.org/abs/gr-qc/9402027). ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 10, 2008, 8:17pm UTC](https://boards.straightdope.com/t/explain-fractal-geometry-like-im-an-idiot/471052/62 "2008-11-10T20:17:00Z")
Yeah, that’s it. So many journal resources are subscription-only, that I had forgotten that the arxiv is open to everyone. ---
**Author:** ![Nicolas\_Bourbaki](https://avatars.discourse-cdn.com/v4/letter/n/ecc23a/32.png) [@Nicolas\_Bourbaki](https://boards.straightdope.com/u/Nicolas_Bourbaki)\ **Post date:** [November 12, 2008, 9:52am UTC](https://boards.straightdope.com/t/explain-fractal-geometry-like-im-an-idiot/471052/63 "2008-11-12T09:52:59Z")
Ooh, a fractal thread! I finally have an excuse to show off cool stuff I learned in Chaos Theory last quarter. First cool thing: Look at the binary expansions of the points on [0,1]x[0,1]. If the ordered pair is of the form (0. **1** a2a3a4… ,0. **1** b2b3b4… ) leave that point white; same for (0.a1 **1** a3a4… ,0.b1 **1** b3b4… ), and so on. If both numbers have a 1 in the same place anywhere in their binary expansions, leave it white, otherwise paint it black. An obvious consequence is that there can’t be any black points in the upper-right quadrant square, or the upper-right subquadrant of the quandrants, and so on. If you want a less mathy idea of what just happened, think of quartering a square, removing the top right piece, quartering the three leftovers, and removing the top right square from _them_. Repeat this procedure an infinite number of times, and you’ll end up with the same collection of points. Now here’s the crazy part: what you get is just the Sierpinski gasket, but made out of right triangles. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [November 12, 2008, 10:50am UTC](https://boards.straightdope.com/t/explain-fractal-geometry-like-im-an-idiot/471052/64 "2008-11-12T10:50:48Z")
So (0.1000…, 0.0111…) is black but (0.1000…, 0.1000…) is white? Yeah, I know, easily dealt with, but I felt like having some pedantic fun. 🙂 ---
**Author:** ![Nicolas\_Bourbaki](https://avatars.discourse-cdn.com/v4/letter/n/ecc23a/32.png) [@Nicolas\_Bourbaki](https://boards.straightdope.com/u/Nicolas_Bourbaki)\ **Post date:** [November 13, 2008, 1:41am UTC](https://boards.straightdope.com/t/explain-fractal-geometry-like-im-an-idiot/471052/65 "2008-11-13T01:41:53Z")
Well yeah, you got the ide- . . . **i see wat u did there** Okay, if the sequence of ones in your example terminates, then we’re cool. That’s kinda why they call [0,0.1) a _half-open_ interval. well okay maybe not _why_, but you know . . . I liked it better when _I_ was the pedant. [Previous page](https://boards.straightdope.com/t/explain-fractal-geometry-like-im-an-idiot/471052.md?page=3)