Exponential map example, 2010 Dec 21
Exponential map plot of Mandelbrot image at coordinates: -0.162 454 183 420 267 275 971 + 1.040 885 052 665 405 201 802 i, size: 7.2×10-18, nmax: 2000000
Numerical errors are apparent at about radius 2.5×10-30 (look for the word FLAWS). These are caused by trying to use F107 precision beyond its effective range. In theory F107 (which has 107 bits of mantissa precision) should be suitable for resolving features as close as 2/2107 = 1.2×10-32, which means it should be fine in a 1024-bit wide exponential map image down to radius 2×10-30. That is in fact usually the case for fairly "undemanding" images like the Munafo midget, where the number of iterations is fairly low.
This view is more demanding mainly because the number of iterations for each pixel is much higher, and roundoff errors gradually accumulate with iteration.
| (scroll down...) | |
 | radius = 1.3×10-36 |
 | radius = 6.94×10-34 |
 | radius = 3.72×10-31 FLAWS FLAWS FLAWS |
 | radius = 1.99×10-28 |
 | radius = 1.07×10-25 |
 | radius = 5.71×10-23 |
 | radius = 3.06×10-20 |
 | radius = 1.64×10-17 |
 | radius = 8.77×10-15 |
 | radius = 4.69×10-12 |
 | radius = 2.51×10-9 |
 | radius = 1.35×10-6 |
 | radius = 0.000721 |
 | radius = 0.386 |
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