Fractal Waves

Tuesday, 14 July

I’ve been reading a great book suggested by Andrew called Chaos: Making a New Science.  It is about the discoveries/unification of chaos theory and complexity science (Lorenz attractors, logistic map, fractals, etc).  A lot of these pioneering scientists were studying turbulence: weather or fluid dynamics.  This book has been a nice complement to my daily walks/jogs along the beach, where I’ve been paying particular attention to all the patterns!

As Benoit Mandelbrot pointed out, Hokusai, the famous Japanese artist, shows the fractal nature of waves – waves within waves within waves (and fractal patterns in the cloud outlines too!)

Hokusai - The Great Wave

Waves around Koshima.

What scale is this pictures? Kind of hard to tell! 

These patterns are amazing.  Sand or carpet??

Eventually, I got an idea:  if I couldn’t study monkeys because of the waves, why don’t I study the waves?  They have fractal patterns too!  At first I was half joking, but the more I thought about it, I decided, why not?  Maybe it could give me some data to play with!  I’m going to study fractals, darn it!  With or without monkeys.

My original plan was to sit out and collect data on waves as they passed by – time series of the waves and possibly height, if I could plant a yardstick in the sand.  The plan began evolving as I started thinking about what materials I had.  I had rope.  There were ample abandoned buoys, bamboo sticks, and rocks on the beach.  I had a waterproof bag.  I had an iphone, which had accelerometers inside of it.  Maybe there was an App I could get that could extract this data?  There totally is!

Today I gave it a try: iphone in 2 plastic bags inside a water-proof bag which floats if filled with air, wrapped around a large stick stuck in the sand.  I attached a second rope to the bag and a rock planted further up shore, so if the stick breaks or falls I won’t lose my phone.

My first time planting the stick it had fallen over by the time I got back to my beach mat, and no data had been recorded by the app : /  I found a large rock to hammer the bamboo further into the ground, which lasted the rest of the time.  After a little over an hour I took it down to check out the data.  Success!

Supplies.

A version of the contraption.

New study site? 

Now THIS is the way to collect data!!

I have no idea what this means or how to interpret accelerometer data, but I have data! (And, something to do during the impending typhoon!) 

raw data

My hope is to collect more data, come up with a plan for refining the data to get at wave magnitude, and running fractal analysis on the sequences to see what wave magnitude scaling might be like.  Previous studies have actually used this type of analysis on off-shore ocean waves height, with hopes to better understand wave patterns to inform breakwater design (shore protection, offshore platforms, etc).  I don’t necessarily expect to produce anything that would be that useful or legitimate…right now all I have is a make-shift ocean powered pendulum…but it will be a fun fractal side project while I’m waiting!  I hope to improve on the design tomorrow, possibly using some buoys I collected on the beach.

New life philosophy: when life gives you lemons…measure them!