There are many paradoxes—occasions when two seemingly mutually exclusive truths coexist—in life. Pinocchio saying “My nose will grow now,” is one theoretical example, because if he’s lying, his nose will grow. But that would also mean he just told the truth, in which case his nose wouldn’t grow, meaning his nose would somehow be in a state of simultaneous growth and no(se)-growth.
Some fascinating physical representations of paradoxes are theoretical fractal shapes, like the “dragon curve” fractal Oscar van Deventer used in his latest puzzle creation.
The reason a theoretical fractal shape (like the “dragon curve” van Deventer modeled his puzzle on) could be considered a paradox, is because it simultaneously has an infinite perimeter, as well as a finite area. This effect is achieved by repeating a single pattern over and over again on an ever-shrinking scale. A well-known fractal pattern, as well as a good example of this effect, is the “Koch snowflake” below:
With each new iteration, the shape gains more and more sides, hence more and more perimeter. But because the new shapes developed by increased perimeter keep shrinking, this infinitely layered shape could fit in a finite circle.
And although van Deventer’s puzzle is certainly not infinite—it only has nine pieces—it does evoke a pretty cool effect of making each large puzzle piece “shrink” to fit into a space one wouldn’t think would be large enough. And when he drops the final piece into his puzzle in the above video, it does briefly look like the piece has disappeared, as it essentially goes from being discrete to indiscriminate.
Perhaps the most surprising part of fractal geometry in general, is that it is not only theoretical, but is in fact seen quite often in nature. Trees, snowflakes, and coastlines can all serve as examples of fractal geometry, right down to the atomic level. I.e. look at a snowflake at one level of magnification, you see a certain pattern. Look at the next level of magnification, you see the same pattern repeated. And the next level. And the next, and on and on.
It seems as if the puzzle of nature is infinitely complex, while the mind is infinitely determined to put the picture together, one piece at a time. Or nine pieces in the case of van Deventer’s puzzle, which, if you’re looking for a super late Christmas gift, will cost you about $55.00 bucks.
What do you think of van Deventer’s puzzle? Does it make you rethink fractal geometry, or with only nine pieces does it not quite cut it? Let us know in the comments section below!
Feature Image: Laser Exact!
Fractal Image: Wikimedia Commons