Patterns and Math

 You know I love things with patterns. Some of them can even be described mathematically. Maybe that's one reason I like sempervivum a lot. Here are three from my rock garden that have somewhat different growth patterns.

The first one is 'Gold Rush.' It's looking pretty happy, and is keeping its yellow color. This pattern is most typical of Sempervivum. Some are even spread open a little more, although they all tend to tighten up and circle the wagons, so to speak, when left outside as the weather cools.

This is Sempervivum arachnoidea. It has the "spider webbing" which shows up clearly at this time of year. They are tightly curled almost into a ball.

But my favorite at this time of year is the Sempervivum globiferum. I had nicknamed them 'Roly Poly' for years until I found their actual name. To make babies they send out little balls which roll away and then take root. But here is a large (for this species) established rosette. Can you say Fibonacci?

This isn't a repeating pattern like the above, but it was very cool to find. Unfortunately I couldn't get a good picture without a clear background, and then the whole thing took on that color because it's nearly transparent. Actual size less than 3/4 inch across. This is a clammy ground cherry seed pod that has become skeletonized. That means all the tissue has decomposed except the veins, which are harder. Skeletonized leaves are also very cool to find. It has to be somewhat mathematical because veins, tree branches, etc. all follow fractals.

This is a water pattern from the other day. All of these are examples of wave patterns as the light is reflected off the surface of the water when waves (ripples- waves and wave interference, etc) are formed.

Finally, this is simply a pattern of completion. I figured I should show the violet seed pods before they open. There are two little pods hiding among the stems and leaves. Remember the seed pods opened into three parts? I just realized that's a little odd. Violets are dicots (two baby leaves). Most monocots (one baby leaf) have three-part pods. Not so much with dicots. I'll have to think about this some more.

Mostly, I worked on the last weeding of the rock garden for the year, and played with my database.

See Clammy Ground Cherry See Common Blue Violet Seeds