Julia set flower, at the limit of double precision

[Duncan C]

The image above is a Julia set, rendered in 3D using distance estimate values to calculate the height of each pixel in the image.

The image is at a real width of 2.51E-13, which is right at the limit of double precision. At this zoom level there is a fair amount of noise introduced due to cumulative floating point errors. I usually reject images when they start to exhibit floating point errors, but in this case, I rather like the effect. It looks a little like Perlin noise.

I reworked a test version of my program, FractalWorks, to use "long double" (128 bit) math, and the noise on this image disappears, but I like the effect as it is.

(I actually have a fair amount of work to do to support user selection of double or long double precision. My app's native file format uses double precision, so plot coordinates are not specified with enough precision. My test version only changes the inner iteration code to long double; the rest still uses "regular" double precision)


Regards,

Duncan C

[Nahee_Enterprises]

The image above is a Julia set, rendered in 3D using distance estimate
values to calculate the height of each pixel in the image.

As you state, even with the noise it works well for this image.  And the colors came out quite well also.

Wonder how this one would look as a anaglyph.