Gave it my damnedst. Most of them are actually pretty close the first one not as much. Its more of a guide guys not a rule. Very simply people find things within the ratio beautiful. Many artists create within the ratio without being aware of doing so. I found this very true early on in bonsai. When I started the "Golden Ratio" thread. I gave it up because despite the negative response and disbelief that the ratio has no place in bonsai, ITS EVERYWHERE from Kimura to Pall to Hagedorn to naka. everyone of them has a tree or multiple trees in the ratio, The famous Kimura planting on the slanted rock falls into it. The is no point in arguing fact. The ratio is everywhere. Whether you choose to feel that it is a factor that should be considered in bonsai is irrelevant the ratio was here before we knew what it was and it will keep on being a part of nature after we're gone. Since bonsai is a natural art you would have to intently try to remove the ratio and even then you wouldn't be able to, assuming a conifer exists on you bench regardless of species, the ratio is at work, in the development of whorls and branches, the growth pattern of the needles down the branch, and finally in the cone itself.
Young'n out.
You guys are missing the huge point.
No one will disagree with finding a sequence in a tree after it is designed. A chimp can do that given enogh instruction and an endless supply of banana's. Show me the artists out there styling trees with a ruler and a sliderule. Not all bonsai is about natural. I would say most of it is stylized in fact.
I would suggest using the trees I posted and doing virtuals on how they might be improved using the sequence. In fact if some could even verbalize that it would be cool.
Once again to quote Greg: it would be cool if some advocates could explain why these trees are not natural even though they are mostly unchanged since their days in the wild and are "natural" growing plants.
"I would think three of them would be improved if they HAD more natural balance - and looked more like something you would find in nature."
I do not see how this advances the dialog either.
If all that is necessary to making better bonsai is the application of a ratio, then once again a chimp might do it with more banana's. These rules you so eloquently speak of may be universal and etched in stone as deeply as physics, but not everyone is Hawking.
I propose a deconstructing of the trees I posted and make them more deftly fit the Golden Section so they might be more to the liking of nature. Since the rules are everywhere and as old as the universe itself, this should be a very easy exercise for its advocates.