Symmetry is over rated. “Was it a car o” What’s that you say, a palindrome? Oh then did you mean “Was it a car or a cat I saw?” If something is symmetric, you need to see only part of it. The rest is implied by symmetry. The leaf in the featured photo looked perfectly symmetric, so how should I present a photo? I decided to go with the rule of thirds, and put the backbone to one side. You don’t have to see both halves of the leaf to imagine how lovely the leaf looks. But the truth is, it is a slight lack of symmetry which makes the photo interesting.
When I saw this Angled Pierrot (Caleta decidia) hanging below a leaf one morning I decided not to wait for it to spread its wings. The patterns on the two halves of its body are identical, and a photo with closed wings is enough to let you identify it. It was happy to play along by presenting only one antenna to me. But it didn’t manage to place both hindwings identically over the forewing, so you can see two of “tails”, the little bits of the hindwing which jut out. More broken symmetry; will nature never be perfect?
And the moon? Gravity pulls the larger moons and planets into visually perfect spheres. No natural object that you photograph will be as perfectly a sphere as the moon. But even there, if you look carefully, you’ll see craters and mountains on the surface. You may call them blemishes, but they are what gives it that look of yoghurt setting slowly in a bowl, releasing bubbles as it forms. I love those blemishes.
And then there is hidden symmetry! This lovely eight-petalled daisy called me to take a photo. Eightfold radial symmetry, is it? No, it was a complex flower like any in the aster family (Asteraceae). Which meant that each flower is actually an inflorescence fused together. Eight of the outermost flowers, the ray florets, give rise to the large showy petals. The rest, the disk florets, are clustered together into the eye at the center. There, in the eye, you can see one flower has opened up and shows clearly the fivefold symmetry underlying the complex flower. If you turn the flower over and look carefully at the bottom with a scalpel and magnifying glass in hand, you’ll see that the ray florets also have the same fivefold symmetry,


Islamic art of the 16th century CE developed a fascination with interlocking and hidden symmetries. The example on the left is a pattern from the dome of Humayun’s tomb in Delhi, designed by Mirak Mirza Ghiyas. On the right is a pattern from the central arches of Mihriman Sultan Mosque in Istanbul, designed by the Turkish polymath Mimar Sinan. The two are nearly contemporary: the tomb in Delhi completed in 1558, and the mosque in Istanbul in 1570. The artists know that symmetry is a wonderful organizing principle, but somewhat boring. So they hide other things inside the outer pattern: flowers and leaves in one case, calligraphic writing in the other.
This post is scheduled to appear while I travel. I’ll reply to your comments and look at your posts when I have network coverage.




















