Tree Branch Self-Similarity

Trees are beautiful when they are lush and green in summer or when they flare with red and gold in autumn. What about winter, when the branches are bare? That’s when it’s easiest to see the self-similar structure in the tree’s branching habit. At each juncture where a bud begins a new branch, the angle of the branch is determined by the tree’s genetics and specific influences in the environment. Each tree species has a standard pattern, which is repeated with every bud, so that the shape of the junctures is the same, broadly speaking, in everything from the first heavy branches on the trunk to the newest fine twig. I’ve talked about this before, but I just can’t get enough of the beauty of these elegant patterns.

There are important biological factors behind a tree’s branching habit, but from a mathematical point of view it reveals a fractal pattern, which has the property of being self-similar. A self-similar structure looks roughly the same at every scale from the largest zoomed-out view to the narrowest closeup. There are practical limits in the real world (if you zoom in far enough you get to individual cells and eventually molecules, which aren’t particularly similar to the tree trunk), but within the range that we can call the tree structure the idea holds. If you zoom in on the picture above each branching region looks like the overall structure of the tree.

Fractals are important in nature and mathematics (as I’ve commented before). They are also very beautiful, and reveal the beauty in the structure of everything around us.

Posted in response to the WordPress photo challenge: Structure


My Cozy Corner

Isn’t this nice? This is where I’m usually found when my husband is out sailing (and you can just make out his boat above the chair in this image). The marina where we keep the boat sets up this gazebo each year, and I sit there in the shade, enjoying the view and the breeze, with my book and laptop and iced tea, and it’s wonderful. Sadly, this year they never put the gazebo in place, because the water level in Lake Ontario is so outrageously high that the ground never firmed up enough. I spent hubby’s sailing time either in the car or in the marina office, but neither spot is as comfy as the gazebo. I’m looking forward to settling back into gazebo bliss next year, though.

Posted in response to the WordPress photo challenge: Corner

Gorgeous Light

I’m a sucker for clouds, with hundreds of sky photos in my folder. Here’s a shot I love of the gorgeous, golden light on the buildings and clouds opposite the setting sun. This time of day is often called the golden hour because of the color of the light, and it creates a warmth that you don’t see at other times. The view stopped me in my tracks. I hope you enjoy it as much as I did.

Posted in response to the WordPress photo challenge: Shiny


First of all, I want to acknowledge that there are actually 118 known elements, not just four! But I’m happy to play along for the purposes of this week’s photo challenge and focus on just the four “classical” elements. Here you have them all in one image! Rocks and plants in the foreground (earth), clouds up in the sky (air), the sun (fire), and Black River Bay off of Lake Ontario (water). I hope you enjoy the pic!

Posted in response to the WordPress photo challenge: Elemental