Can you "expand" your thought on squares?

This question is in regard especially to the image Baileau III, discussed at http://fractovia.org/bb/index.php?topic=15.0

 In this particular image, as with a great number of fractal images (ah, and notice my use of image instead of picture, to bring up an older thread), we see a fairly symmetrical fractal; that is, if I copy the image into Photoshop and rotate it 180-degrees, it looks fairly like the original image (as opposed to a 90-degree rotation, but a great many fractals will look very similar even after a 90-, or even 45-degree shift).

 (There are a number of differences, but they are fairly small, considering all things.  For the most part, it is a twin.)

 This raises the question, then, of whether symmetrical fractals, of which I'd argue a vast number of fractals are, would best be presented in a square canvas.  Does the very nature of a symmetrical fractal impose a certain constraint upon how the canvas should be sized?

 Perhaps it's a question of aesthetics.  In your comment, you pointed out that you like the yellow in the two opposite corners.  I replied that I would have liked to have seen the yellow in all four corners.

 Having not seen the image presented on a square canvas, how would I come to expect (and rightly I think, again not really knowing, but rather just presuming) yellow in the two hidden corners?  I'd respond that it's because the nature of the fractal suggests that I would in fact see yellow in those two corners.

 Looking closer at the fractal, however, I'd see that the four corners would not match up 1:1.  Rather, they would match up diagonally - 2:1.  I need merely move my way from the four corners - two shown, two hidden - to the 'heart'/middle of the image to see that the two hidden corners would actually be larger than those shown.

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 Perhaps, however, the rectangle <em>is</em> the best way to present this image.  When we first look at the image, I think we notice the horizontal movement, as opposed to the vertical movement; this is a flight of stairs that we are looking down at, watching as the steps go further and further into the depths of the earth.  We, as earth-bound creatures, would walk around the column sinking into the ground, for that is where the stairs are put.  We'd in fact start to our right to go in deeper, so to the right we look.

 On the other hand, if the image was square, we'd start in a corner instead, or perhaps at the bottom, neither of which is what we'd really want to draw attention to.

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 Which leaves me at a stand-still (oh what a surprise).  Square canvas seem to be what fractals would like to reside in, by their very nature, but man being man, perhaps our imposing of rectangles upon them is a sign of our creativity and our desire to move the natural to the beautiful.

?

~James

Two times I have tried to post a reply to this message: one time in Linux, one time in Windows. The two times it has been in two different computers 15 miles apart. The two times the computers have frozen up (yes, one in Linux, and one in Windows, both frozen up, locked, dead). Two times I have lost everything I have written in: one time a very long message, the second time an entirely new message with some additional ideas. I can't believe it!!    I think that's too much. This is outrageous!!!  The ghost in the machine is sabotaging me... f--k!

No yellow in the two now-displaying corners ...  Hmm.

 So, my assumption of how the fractal would look is wrong, in that there's no colour.  The design, however, is still correct.

 The question still remains whether a square canvas is the best for fractals, as fractals, and if a rectangular canvas is imposed by man for looks.

 But, in this case, the rectangle canvas looks better ...

If the rectangle looks better in this case, then it's a matter of aesthetics, don't you think? Personally, I think it looks horribly in the square.

Actually, one of my obliterated ideas concerned the presentation of symmetrical fractals such as this one in pentagonal or hexagonal canvases. Those would be as symmetrical as a square one (if all the sides were of equal length). Yet I think the best "appeal" should be contrasting figure (geometric - the canvas) and form (the fractal picture). Maybe Baileau, in particular, looks better in the rectangular canvas, not because of mere aesthetics (nothing to do with the yellow corners), but because the rectangle is less symmetrical than the square (?).

Anyhow, I don't think it's in the fractal's nature to be displayed in a square canvas, but yet, maybe it's a matter of "tradition" to use a rectangular canvas most of the time. Is our "field of view" rectangular? Is that why the wide screen format is already the next big thing?

I'd say it's rectangle (our field of vew).  As I sit at my desk, typing, I can sense more to my right and left than up and down.

 Good point.

 But does that mean that a rectangle wider than it is tall is better than one taller than it's wide?  It would seem that, everything else being equal, that would be the case.  Most art is laid out on a wider canvas.  A taller canvas requires one to move the head, perhaps even move back ...

Not better, more "natural" maybe. There could be two dominating factors: (1) subject, (2) artist's choice.