The Universality of Curves

It is Ukrainian Christmas today.  With many Ukrainians in Niagara and Ontario, there's a tradition for the rest of us to leave our Christmas trees up for this date.  Ours came down earlier, due to the activities of Baxter the cat.  He started to consider the tree something to take down himself, perhaps a desire to get into the cat Christmas videos.   Our pictures today focus on curves.  As I take pictures of urban decay, I find that the shapes, patterns and lines of wear and tear are the same as those in nature's own processes.  The first picture is wear and tear  on a billboard sign.  The plastic material wears away in arcs and curves.  The second picture is ice, with some abstract filters applied to create the extreme colours.  It too has formed in arcs and curves. I found this explanation for the puddle freezing into ice: "The shallowness of this puddle suggests that it rapidly froze; only a thin water layer remained below the puddle. Then the fast-falling temperatures likely caused the ice to contract, which produced the cracking. Continued cooling widened the cracks. The ring pattern shows that the main direction of the stress force was radial, but the scalloped pattern along the rings shows that some stress varied with angle around the center. The small amount of water that didn't freeze rose into the cracks due to the hydrostatic pressure of the ice above and capillary action. Water in the rings then froze and expanded, and as it did it widened the rings and also directed the remaining small amount of liquid to the top of the ice. The slight bulges on the bottom of the rings were remnants of its last contact with the deepest water. In other words, the unfrozen water at the bottom of the puddle was, in essence, pushed and suctioned into the cracks." from Douglas Stith's website