Fractals? We're talking about fractals? Yes, yes we are.

Recently, I took the family to the Kalamazoo Valley Museum to see their Fractals as Art exhibit...along with all of the other great stuff they have there. I have always thought fractals were pretty interesting, and seeing the results in various forms is always pretty compelling. My kids (5 yr old, and 2 yr old) didn't care much about the math behind them...they just like the visual results. I thought I would use their interest as an example of discussing math theory with them. (*Note: at this point my wife said "why do you always have to 'nerd up' a good thing?"*)

After seeing all of the visual results of fractals, I decided to work out some fractal based designs in Inventor 2012. I am not the smartest guy around...so, I wanted to take at some of the more basic fractal concepts. My first go at it wasn't going to be a Julia Set fractal. I am very confident I could do a Menger Sponge or Sierpenski Triangle in Inventor (or AutoCAD for that matter). Really, I wanted to take a look at doing something very familiar in a different way.

So, I decided on the Koch Snowflake.

The basic idea is a curve without tangents, constructable from elementary geometry with finite volume and infinite parameter. Now, the question was: could I do this in 3D? (and could I do it in a few hours before my son goes to bed, so he can see it).

Now, what I ended up making was not truly a 3D version of Koch Snowflake. A Koch divides each segment in thirds and inserts the original shape (a triangle). I was using triangle based pyramids..and decided to invert the next 'layer' as half the size of the previous pyramid. I hope that makes sense.

After doing some quick layout sketching (thanks Mr. Gascho for my geometry education), I got to work.

In Inventor, I just went with a simple process:

1 - Model triangle base pyramid (via loft to point)

2 - Insert work axis

3 - Create offset work plane for next pyramid creation

4 - repeat as often as needed

Once the initial geometry was built, it was just a matter of performing the necessary Circular Patterns around the existing work Axis.

Now, this is just the start. I could have kept going and added the additional fractal'ation to these areas (again, infinite parameter)...but, the little man was happy with what he saw.

...and I didn't want to risk 'nerding it up' with him too much.

-lw