Puzzle Description:

This image is the third iteration of the procedure that leads to the Sierpinski carpet. The construction of the Sierpinski carpet begins with a square. The square is cut into 9 congruent subsquares in a 3-by-3 grid, and the central subsquare is removed. The same procedure is then applied recursively to the remaining 8 subsquares, ad infinitum. (To get a better feel for these iterations, visit http://www.shodor.org/interactivate/activities/SierpinskiCarpet ). Now the INTERESTING part!!!! If the original square is 1 foot by 1 foot, then after the first iteration, the area is 8/9 square feet. At each step, you are removing 1/9 of the remaining area. So after two iterations, the area is (8/9)^2 (i.e., eight-ninths times itself). Here, in the picture shown, the area is then (8/9)^3 = (8/9) x(8/9)x(8/9). But if we let the number of iterations go to infinity, we are multiplying 8/9 times itself over and over again. The result of doing that is that the area eventually becomes ZERO!

#1: Petra Lassen (stjarna) on Feb 19, 2009 [SPOILER]

Fun puzzle, complicated maths!

Amazing!!!!!!!

Cool. Just like Sierpinski's Triangle!

Reminds me of fractals. Here is a flash actionscript that is only 4k and really pretty:
http://www.zenbullets.com/automatons/Tree.swf

And since we are all into pixels, here is a pixel flash that is less than 1k. (I'll bet Jan knows how to make cool stuff like this.)
http://krazydad.com/bestiary/bestiary_random_pixels.html

Thanks for your entry!

If you like things like this, take a look at this Mandelbrot Fractal video:
http://www.youtube.com/watch?v=WAJE35wX1nQ

Here's a webpbn puzzle (naturgirl's first one) that looks like a Sierpinski Triangle:
http://webpbn.com/index.cgi?id=2025

Nice links, Teresa! That Mandelbrot movie reminds me that as you zoom in on the full-blown Sierpinski carpet, it looks exactly the same as the zoomed-out view.

Watching all the movies inspired me to do a pattern. At least it is in B/W so it won't make anyone go cross eyed.

http://webpbn.com/index.cgi?id=5094

Would you believe I was thinking Sierpinski as soon as I read the title?

Excellent!!

I hadn't heard of this pattern, so I just thought it looked cool, so it was nice to discover it's cool /and/ interesting :D

Math math, blah blah blah... LOL

Echoing Adam.

On the one hand there's something interesting about pattern solving where, when a solve is done in one place, one can move over to the repeating iterations and solve them. On the other hand, it gets boring after a bit and one is no longer logically solving the puzzle.

The math in the description, in the long run, is more interesting than the puzzle. But on the whole it was worth the effort.

I once wrote a program on my TI-81 that generated a Sierpinski triangle. That was fun! This puzzle, as a puzzle, not so fun - but I enjoyed reading about the math. :)

The math part really made this puzzle worth solving. I enjoyed reading the explanation.

I think that infinite processes take forever. Also, the area of the rug only approaches zero, but I don't believe it actually becomes zero.

Goto next topic

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