Monday, February 21, 2011

Koch Snowflake (Base-Motif Fractal)

It warmed up late last week. It was wonderful! Virtually all of the old ugly snow melted over the weekend. It was great to look out the windows and see something other than white. The skies were blue, the sun was shining, and the birds were singing. It was great...while it lasted.

As I sit here this Monday afternoon in February, there is yet again another winter weather advisory. It looks like a blizzard, and from what I hear, the snow isn't supposed to let up until after midnight. Great.

Speaking of snow, here's a little diversion we took last week. Instead of getting out the Algebra books, we decided to try our hands at creating fractals. We each chose one and spent a couple of hours being creative. I have to say, it was a lot of fun!

This is a Koch Snowflake...

We neglected to take a photo of the first nine inch equilateral triangle, but I think it's easy to see it. During the first iteration, every side of the triangle has been substituted with a base-motif. The line you see running down the middle is where two pieces of construction paper have been joined. That line ended up helping keep everything plumb.

Because there's a lot of drawing and erasing required for this fractal, it's best to start out with light pencil lines. Light lines make erasing easy, but viewing photos more difficult. Sorry about that!

The first triangle is the first iteration. The photo below is the second iteration.

In the third iteration, each of the 12 line segments have been replaced with the base-motif again.

And again... (fourth iteration)

fourth iteration finalized...notice the inside corners?

and yet again... (fifth and final iteration)

Isn't that cool?! This is but a speck in the world of fractals! We could keep going except it's virtually impossible to erase any lines after this point. Be sure to look at this link to get a much better idea of base-motif fractals.

photo credit

Hey, have a happy fractals Monday!

P.S. I just noticed this is my 200th blog post. Wow Wee!


  1. ~*~*~ 200! ~*~*~
    That Is Fantastic! And you do a Great Job!
    I love the pizza one. We had a "Make Your Own Pizza Night" not too long ago. Down in the cabin at Hocking Hills for Thanksguving. When the kids were still home we would do that at least once a month on a Saturday Night. Mary Lou started it and I copied from her. We really should do that more often.
    But I digress !
    (((( Hugs ))))
    Elle Belle

  2. What a cute blog design... I LOVE the font. :) Glad to hear you guys are doing well...give my love to Rachel! (I don't have email here so I can't write her a note.