You have a good question Pete. However, in the wild there are only certain circumstances in which one can see the symmetry you mention. Not many creatures are even roughly symmetrical about more than one plane. Also, can be surprisingly difficult to spot symmetry if it is not horizontal or vertical with respect to your own axis. A random plane of symmetry often vanishes into the background more easily than one would believe. Some of course are not clearly symmetrical at all; consider many flatfish and gastropods. Certain other molluscs that are largely symmetrical, disguise their symmetry breathtakingly. Consider the dynamic changes of colour and texture to be seen in octopuses and cuttlefish.

Now, in my line I have had occasion to encounter more examples of camouflage than most participants to this blog (have I taken a census? No, that would anyone like to take bets?) What I am not certain of is how often I have cracked an instance of camouflage specifically because the creature was symmetrical. (Of course, I have no statistics whatsoever on the proportion of creatures that I have missed altogether. All I can be sure of is that they probably outnumbered by a large factor, the creatures that I successfully searched for. One reason that I am so confident of this is the number of times that I cracked camouflaged by accident and was dumbfounded by its quality. Another is the number of times that I left for just a few minutes, and subsequently could not find the creature again, even after a concentrated search.)

Now, symmetry is by no means the only, or even the major, camouflage breaker. It was the subtlest discrepancy in the density of a clump of foliage that enabled me to spot a pair of tawny frogmouths. I often have discovered stunningly camouflaged caterpillars simply because they did not camouflage their droppings. (Am I being too greedy? I hardly think so; some kinds of caterpillars and grasshoppers for example go to a lot of trouble to achieve long-distance disposal of their wastes in ways that do not betray their presence.)

But back to symmetry.

In Australia I saw a bird dropping spider, not one of the usual brown jobbie, but a black-and-white crab spider so well camouflaged as a bird dropping that I was fooled even when examining it through a lens. It took me some time to realise that there was an (oblique) axis of symmetry, and that I was looking at a spider.  Many sticky-looking brown bird-dropping spiders (in another family) do in fact have asymmetric markings that aid the resemblance.

In South Africa I have seen a stunning example of a long-horned grasshopper, so well camouflaged on tree bark that even once I had spotted it, I could not see the head till I had caught it. In that case the clue was symmetrical, but I am not sure that the symmetry was the clue. What I noticed was a subtle pattern that whispered "legs" to my entomological inner eye.

Thanks Jon. Flatfish is a good one - I didn't think of them.

I'm wondering about you inspecting bird-droppings through a lens. Is this a particular interest of yours? (Mind you, I'm just realising that I've done the equivalent myself - but with regurgitated pellets).

Of course, everything you say is correct, but it still leaves us with the multitude of insects that lack exotic camouflage. Irish insects seem to be pretty unimaginative in that respect (i.e. mostly lacking exotic camouflage), but that is no doubt a result of the evolutionary pressures they experience. One would have to examine predator/prey relationships on a species-by-species basis rather than assuming, "I can see him why hasn't he been eaten?".

As for me, I'll continue to examine each blemish and spot with nervous eyes because I have a paranoia about bloodsucking parasites.

Not actually an interest specifically. I just happened to spot a spot on the white leaf of a Eucalyptus macrocarpa in Perth's King's Park botanical gardens in Australia (Don't miss them if you go that way. Almost as good as Kirstenbosch! Not just a good range of plants, but a fine showcase for Aus's terrific ranges of related (or unrelated, but closely resembling) plants. Stunning!)

Anyway, I idly inspected it in passing and dismissed it as a dropping, but something bothered me. A closer look did nothing to enlighten me further, but I got suspicious, took out a lens and inspected it to see whether there was anything interesting. Nope... And only then did I spot the symmetry (off axis, as it happened). After that it was just a matter of systematically inspecting it till I could  make sense of what I saw.

We saw the Cirque Soleil in Perth as well, and pretty surreally fabulous it was, as always, but in my book that spider had them well beaten!

Talk about unfair competition!