Wishing everyone a happy New Year in this, my first post of the new year! 

 I haven't posted in a while because I caught a horrible cold about a week ago and it is still lingering. So mostly I've been sleeping, reading, drinking tea and blowing my nose.

Today however, I went for a walk with my dog and found some wonderful examples of fractal design in the moss clumps on the ground and hanging from our California Live Oak trees. If you are not familiar with fractal design here is a definition I found on the internet: 

"A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop."

So if you look at the structure of the moss in the picture below, 

you will see the pattern repeating in a variety of sizes differing in length and width.

In the picture below, the moss looked like a wall hanging suspended from the branches.

 I like to think of this moss as 'Nature's Lace."

I've always been fascinated by fractals. In researching them today I came across a very interesting tidbit that I had never read before.  It came from the following website:

https://gabrielhemery.com/tree-fractals/

"In the 15th century Leonardo da Vinci wrote:  "All the branches of a tree at every stage of its height when put together are equal in thickness to the trunk."  The website goes on to say, 

"So, if you were to cut all the branches off a tree at a fixed distance away from its trunk and bundle these all together, the size of this cylinder would equal the size of the trunk (and any branches) below. The rule applies at whatever distance (or height) you exercised this - now that's cool math!"

This is known as 'Leonardo"s Rule for Branches.'  If you google that, you will find all sorts of fun information and people who dispute his theory and talk about

 how the formation of branches is more related to wind.

Anyways, something fun to ponder and wonder about. And now, it's time for more nose blowing

 and another cuppa to calm my cold.