Real MATHEMATICS – Strange Worlds #13

Love of Dinosaurs

I loved reading weekly television guides when I was a child. Thanks to these booklets I knew when to catch my favorite cartoons and movies. This is why I was able to watch some great movies such as Jurassic Park more than once.

Jurassic Park (along with the famous cartoon Flintstones) was the reason why so many kids from my generation interested in genetics, paleontology and obviously dinosaurs. After 1993 when Jurassic Park was a big success, majority of the kids (including me) started learning names of the dinosaurs starting with Tyrannosaurus Rex.

Jhkbi8QKyPml.jpg
My favorite paleontologist: Ross Geller.

Dragon Curve

In my mid 20s I was doing research about fractal geometry and I eventually found myself with Jurassic Park. Apparently in 1990 Jurassic Park novel was first published. There were strange shapes just before every chapter named as “iterations”. These iterations were actually showing some stages of a special fractal:

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This fractal is known as Jurassic Park fractal or Dragon curve. I prefer using Dragon curve because let’s face it; dragons are cool!

How to construct a dragon curve?

  • Draw a horizontal line.
  • Take that line, spin it 90 degree clockwise. This will be the second line.
  • Add second line to the first one.
  • Repeat the same processes forever.

After first iteration you will end up with the following:

20190318_123050

After second iteration:

20190318_123404

Third and forth iterations:

Just before the first chapter of the Jurassic Park novel you can see the forth iteration named as “first iteration”:

One wonders…

You might find these ordinary. Then let me try to surprise you a bit. First of all cut a long piece of paper as shown below:

20190226_123508

Did you do it? Well done! Now unite the right end of the paper with left end:

20190226_123548

In other words the paper is folded in half. Now slowly unfold the paper such that two halves construct a 90-degree angle between them:

20190226_123649

Fold the paper second time in half:

20190226_123720

Unfold it carefully:

20190226_123749

Do the same things for the third time:

And finally repeat the same process for the fourth time:

Conclusion: Whenever a piece of paper is folded four times in half, one would end up with the fourth iteration of the dragon curve.

M. Serkan Kalaycıoğlu

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