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Increasingly Impossible Objects Becoming Increasingly Possible

Topics: Technology | Add A CommentBy admin | October 7, 2010

These 3D renderings of fractals suggest that just around the corner, there’s something just around the corner.

There’s a place I know, just around the corner of the corner of the corner. It’s inside a house designed by Karl Menger , and the walls, floors, and ceilings are covered with carpets designed by Waclaw Sierpinski. I’ve been going there since I was about five, when a Japanese fellow who rented a room from my family showed me how to make a Möbius strip. You’ve probably seen examples of impossible objects before; people are probably most familiar with MC Escher’s work, but there are many other artists who’ve dabbled in this arena. You can even make your own impossible triangle, or if you’re feeling really ambitious, you can engage in a little fractal origami. I love illusions like this, but I’ve always been even more fascinated with objects that can be partially represented in two or three dimensions, but require a little imagination or mental investment to grasp. We’ve touched on hypercubes and extra-dimensional ideas before, but today I ran across something I’ve longed to see for ages, which is detailed, 3D animations of fractals, and objects like the “Menger Sponge” referenced at the top. I became a little obsessed with these forms when the book Chaos: Making a New Science came out in the late 80′s. I spent a lot of time in bars drawing the Menger Sponge (which possesses infinite volume and no mass) for strangers, because it was a great conversation piece with the the right sort of person. But I have to confess that my fascination with mathematical/conceptual objects like this runs much deeper. Much like how – after several millenia of believing that human flight was just a dream – the world changed phenomenally in a short period of time once a handful of people saw the Wright Brothers fly their simple craft, I believe it only takes a handful of people seeing the strange possibilities of these shapes before another paradigm shift will occur. I believe there’s something right around the corner of everything, and that our ability to reach it is right around the corner. Of the corner. Below are a bunch of amazing little clips, mostly animated, 3D renderings of fractals. With – alas – really bad soundtracks. Just turn the sound down and enjoy.

This first clip is a trip through a 3D fractal. Which made me want to see a movie based on a story that takes place in a universe like this. Maybe it could be based on a fractal novel.

Another really beautiful fractal zoom. This is what the baroque era looked like in the 23rd dimension. Unless you’re a Tool fan, you’ll definitely want to kill the sound on this one.

Here’s a trip into a Menger Sponge. If what you’re seeing doesn’t make sense to your brain, look at the graphics and explanation further below.

The Sierpinski Carpet: First imagine a square, divided into nine squares, with holes cut into it like this, with the pattern repeating infinitely.


The Menger Sponge: Then imagine a cube that takes the concept into three dimensions.


This is another trip into a Menger Sponge. It’s reeeeealllly slow. You might want to skip up to a little over a minute, then be patient when it blacks out for a bit. It actually does a pretty good job of traveling inside.

A beautiful “fractal crater”