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One of the problems with fractal images is that a lot of information is lost when the calculation is converted to an image. Even if you save the z-values just prior to escape, changes affected at this level could be seriously compromised by a non-linear color smoothing routine.

We chose to circumvent this problem by converting the output pixels to tiles in the complex plane. These can be transformed at will while maintaining the appropriate colors. In the accompanying images we use the Vasarely transforms we have developed previously; these can be seen here: (The Paradox of Greater and Lesser Infinities)(http://web.calstatela.edu/curvebank/waldman11/waldman11.htm). You might find this interesting in its own right in that it demonstrates 'fractal tiling.' (This is not fractals that tessellate.)

Basically, the Vasarely transforms are periodic perturbations in the radial and azimuthal directions and are demonstrated at the above web page. We have applied the same transformations to one of our images, albeit at a much lower resolution, in the interest of computational time and memory.

Which bring us to the major drawback of the method. Since I do most of my images at ~4000x4000 pixels, that would requite 16 million tiles. I will probably not live long enough to see that compute. In the examples provided, the resolution has been reduced to a paltry ~250x250.

The figure Vasarely Transforms demonstrates a combined radial and azimuthal perturbation with the origin at the center of the image. The image Vasarely Waves demonstrates radial waves only, with the origin somewhere off to the southwest and sufficiently far that the effect is that of a plane wave.

Unfortunately, my animated images are too large to post here. Please visit my page at Pinterest (Fractals Reimagined)(https://www.pinterest.com/cyewaldman/fractals-reimagined/).

I know it's much more time-consuming, but wouldn't it be better to apply this beforehand (if it's possible)?

It seems to stretch and fold the Complex plane, so why don't you just implement the same behaviour and conditions beforehand? Then you don't stretch the resolution of the image, as it can qickly drop down on very stretched parts.

All in all a great approach! Especially the last one looks super cool, like if the fractal itself would twist around, but you can already see the drop in quality.

(By the way, didn't know you are actually a doctor)

Hey, welcome back. I actually started thinking about this after you told me how you had implemented the reimagined fractals. What you suggest might very well work if you started with a uniform initial iterant. But when you try it with a reimagined iterant, it just throws the whole fractal off to never-never-land. I know, I tried it. Remember, that one point about the reimagined fractals is the great sensitivity to the initial iterant. In other words, a small perturbation produced a much larger than hoped for change in the fractal.

Thanks for looking!