Title: "Progressive" zooming in a still picture? Post by: matsoljare on December 03, 2012, 06:25:35 PM Since many seem to be fixated on finding new details in a fractal by zooming into a single spot, has anyone ever tried to incorporate zooming in the rendering of a single image?
Dunno how exactly to put this, but i can think of several different ways. One would be to "stretch out" the distance from the center point in the image, using a logarithmic rather than linear scale. Each "circle" of equal distance from this point would itself be rendered normally, but the distances between each circle would be changed. I hope this description makes sense to you.... Another would be a probably wide, panorama-like picture where the right side is more zoomed in to the left, so we can see the zoom towards, say, a very tiny minibrot as we go from left to right, kind of like the common montages of several pictures of subsequent zooms, but in one continous picture instead of being broken up into several. Or, you could use the distance-and-angle formula to render a panorama where Y represents the angle and X the distance from the chosen center, again progressing logarithmically rather than linearly, for example the center of a particularly interesting minibrot. Title: Re: "Progressive" zooming in a still picture? Post by: Pauldelbrot on December 04, 2012, 12:42:45 AM Well ahead of you there. These two banners do more or less exactly what you suggested:
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=8629 http://www.fractalforums.com/index.php?action=gallery;sa=view;id=10462 Of course, for zooms that are very deep at all, the aspect ratio quickly gets ludicrous. Fortunately, one can coil the strip like a rope: http://www.fractalforums.com/index.php?action=gallery;sa=view;id=8985 http://www.fractalforums.com/index.php?action=gallery;sa=view;id=8942 I have ongoing research in that area now: http://www.fractalforums.com/programming/early-success-with-creating-zooms-from-high-res-mercator-maps/?PHPSESSID=a18d5fcf4266ea529a6d28b17f8a1e43 Title: Re: "Progressive" zooming in a still picture? Post by: matsoljare on December 04, 2012, 08:51:27 PM Interesting, what about my idea of "compressing" the distance aspect while keeping the angle, perhaps turning it inside out in the process?
Title: Re: "Progressive" zooming in a still picture? Post by: Pauldelbrot on December 04, 2012, 09:10:56 PM Interesting, what about my idea of "compressing" the distance aspect while keeping the angle, perhaps turning it inside out in the process? I doubt you can do that and keep the mapping conformal. Without the mapping being conformal, spirals and suchlike get squished and smeared into toffee. |