Creating order from chaos...

We have been diving headlong into an amazing rabbit trail of maths, and science and art and if I don't share with you some of these thoughts and experiences and links they will be lost forever like much of the mists swirling through my brain!

The chaos that is my dining table!

And there is SOOO much good stuff whirring through my brain that I don't know where to logically start and how to group it all so it might make some sense, so instead, I think I will just let you follow our story - our rabbit trail that led to so much good stuff...and maybe, you will like some of it too!

After viewing Vi Hart's diatribe on parabolas, the kids were keen to actually graph some parabolas. But before we actually got to that, Hubby wanted see the video, so we watched it again, and that led us to reviewing the ones on spirals and fibonacci:

As we were watching, Video Boy grabbed the graph paper (because you always have spare graph paper lying around, don't you?) and started experimenting with the fibonacci spirals shown in the video - he calculated the fibonacci sequence and used it to guide his rectangle drawing and measuring:

Both kids then started to use the graph paper to join up lines within each rectangle to create a pattern:

Video Boy also did some maths doodling involving square waves and cylinders:

And some random patterns:

Wombat Girl is a bit more analytical, planning out her pattern and carefully translating it onto graph paper:

We then looked at another Vi Hart video (she is unbelievably good - even if you have to pause, rewind and think to fully grasp what she is on about!), this one about Fractal Fractions:

In it, she talks about a iterative process called ABACABA - Wombat Girl loved it and immediately set about continuing the pattern:

We also had a quick look at the ABACABA link on the YouTube page. Did you know that the ABACABA pattern shows up in maths, geometry, poetry, art and music? There is even a book which includes a picture of a Klein bottle (4 dimensional geometry, anyone?). 

I also got into the act, re-creating the phi-flower using the Golden Angle, starting with red (primary colour), measuring 137.5 degrees, yellow (primary colour), 137.5 degrees, blue (primary colour) and adding leaves every time that were a mixture of the colours they lay between: 

Now Phi is an "iterative" fraction. This led me to thinking about fractals. I had this old video tape from 1988 lying around. So I fished out the old VCR from the shed, and we watched a documentary about Chaos and fractals. It was pretty cool. And then Video Boy opened up the iPad and showed my this cool app called Trees of Life which creates trees using iterations:

So then, we watched Vi Hart (again)'s Binary Trees:

...and straight away Video Boy did his own:

Sierpinki triangle!

There are huge number of iPad apps that you can download load (just search for "fractal") which allow you to explore fractals, create them and even look in great detail at the most famous fractal of all - the Mandelbrot Set (and did anyone else notice the cardoid shape that was in Vi Hart's video about parabolas?).

Computers being all clever nowadays, mean that you too can get into fractals and learn some programming at the same time (maths - tick, technology - tick, logic - tick, art - tick) via the very clever people at Khan Academy (can anyone say self-repeating?).

Well now. That all got a bit heavy (but pretty), didn't it? We did some other stuff too...

We enjoyed watching Test Your Brain - Perception, which shows just how fascinating our brain is in trying to make sense of the world.

This led to Wombat Girl showing us V-Sauce's amazing video This is Not Yellow (watch if you want your mind blown):

Did you love the art? (Helena, I'm talking to you!). Did you notice the gorgeous Escher stuff at the end? Because we watched this on iView too (Little Brother - did you notice the Jean Michel Jarre music?).

And just in case you were wondering, yes. We did, in fact, do some work on parabolas. Both the boring way by hand, drawing up cartesian planes and labelling them, and also using Maths GV graphing software I downloaded. Wombat Girl is currently trying to figure out how to graph a circle without looking up the equation.

So after all that chaos, I dare you to look at a tree again in the same way and not be amazed by the wonder of the world and the interconnectedness of it all...

All I can see is fractals...

PS: Some of the more observant may have noticed my beautiful fractal image in my blog header has disappeared. I was playing around with the design, when Blogger informed me that I had used up all my storage on Picassa and it wouldn't let me load the image (or anything else) into the header. It does not give me the same message when I upload pics to my posts...so go figure. One day I may figure out Blogger.