Initial thoughts on a square image canvas for fractals

• June 9, 2006
• James Skemp
• article, software

I've been a part of a number of boards in my years, but the one that I've probably stayed on with for the longest is the board at Fractovia. In response to an image, I mentioned the canvas which turned into it's own thread (Squares?). Here's my intial reply, which I just had to save:

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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 is 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.

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~James

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I encourage you to visit Fractovia if you have any interest in fractals - he's still got the best listing of fractal programs available.