Fractal Mountain Zoom

The origin of the Fractal Mountain area is set to X=-2702km, Y=1574km (scale length 20km) while the observer's view direction point to an altitude angle of -2.832008° (somewhat downwards) and an azimuth angle of +314.537679°, i.e. somewhat northwest. This is the exact position of a small ridge on a mountain more than 60km away from the observer.

Such views are a comprehensive test for the fractal terrain raytracing code, since it 1) should be fast 2) should no miss any ridges.
The current Fractal Terrain/ray intersection algorithm uses a four-level mechanism:

• Grid Intersection at quadratic subareas at the largest scale, about 20 areas per fractal unit (== valley size)
• Superresolution Subdivision: Linear extrapolation with maximal slope estimation, which is similar to a large scale bisection algorithm.
• Resolution Passing: The ray passes over the Fractal Terrain at resolution limited step size until a sure intersection is found.
• Final Bisection: When the previous levels have detected a sure intersection, this last step is performed to trace down the exactness of the point of interest to an atomic level of detail, corresponding to a numerical precision of 10^-10.

The image series also demonstrates one characteristic feature of procedural textures (as fractal mountains may be considered as threedimensional textures), the adaptive level of detail: The larger the zoom scale, the more details come into existence. "Existence" means, that at large zoom scales more details do not merely appear (which is trivial), but that they are computed if and only if they are visible. E.g. at 10° scale the Fractal Terrain is constructed by 11 fractal octaves, whereby at the largest zoom scales shown here up to 35 fractal octaves contribute to the Terrain function. The details of the fractal terrain are computed just up to the resolution limit of the current sight ray.

Mzoom100 (000d 00h:17m:46s): Wideangle overview (100°) of the mountain area of interest. Each following third image will be 1/10th of the previous one, starting with 100°, 50°, 20° images.
Mzoom50 (000d 00h:30m:37s): Normal lens view, horizontal view angle is 50°. This image scale corresponds to that one of a photographic standard lens, a focal length of 50mm for usual 35mm cameras.
Mzoom20 (000d 01h:07m:51s): Slight zoom into the mountain area along the preceding valley. Horizontal view angle is 20°.
Mzoom10 (000d 01h:57m:08s): Teleobjective view along the value. The equivalent focal length for a 35mm camera were about 200m, a 4x enlargement compared with the standard lens.
Mzoom5 (000d 02h:13m:19s): Larger teleobjective view, horizontal view angle is 5°. At the corresponding focal length of 500mm mirror objectives become to get used, since they are much cheaper than equivalent refractor objectives.
Mzoom2 (000d 01h:05m:53s): Telescopic view of the central mountain's peak. The horizontal view angle of 2° four times the diameter of the sun/moon. This horizontal view angle corresponds to a focus length of 1000mm for 35mm photocameras, an enlargement of 20x compared to standard optics.
Mzoom1 (000d 01h:07m:51s): This image scale of 1° corresponds to the scale of the quite common Schmidt-Cassegrain telescopes of 2000mm focal length. Unfortunately, air turbulences result in unsharp images most of the time, such that the effective image resolution is quite below the theoretical limit. The pixel resolution of this synthetic image corresponds to 5.6 arc seconds.
Mzoom.5 (000d 01h:17m:19s): `Full Moon` scaled view. The full moon would just cover the complete image area at this `4000mm shot'.
Mzoom.2 (000d 01h:18m:08s): Central telescopic view, the horizontal view angle is 0.2° or 12 arc minutes. At this enlargement, the diameter of the sun or the moon (0.5°) were more than twice the image size. For a 35mm camera, this scale would correspond to a focal length of 10m or 200x zoom.
Mzoom.1 (000d 01h:28m:44s): 0.1° across the whole image, corresponding to 20m focal length. The pixel resolution of 0.5 arc seconds corresponds to the theoretical limit of an common 8" telescope.
Mzoom.05 (000d 01h:34m:03s): At this scale of 0.05° or 3 arc minutes, the planet Jupiter (1' diameter) would use a third of the whole image if photographed instead. The image is near the resolution limit of the human eye, which also is about 1'. This corresponds to 40m focal length or 800x zoom.
Mzoom.02 (000d 02h:12m:04s): 0.02° or 1.2 arc minutes view angle may be called `Jupiter scale'. At this scale the disk of the largest planet in the solar system would cover the whole image field.
Mzoom.01 (000d 02h:26m:54s): The "sub arc minute" image scale starts at this scale of 0.01° or 0.6 arc minutes or 36 arc seconds.
Mzoom.005 (000d 02h:36m:19s): At this scale one would see 1/3 of the surface of planet jupiter. The scale is 0.028 arc seconds per pixel; this resolution corresponds to an optical telescope of 4m aperture at an wavelength of 650nm. The (synthetic) resolution of this image is about twice of the theoretical limit of the Hubble Space Telescope in visible light. This corresponds to 400m focal length or 8000x photographic zoom.
Mzoom.002 (000d 02h:52m:19s): A resolution beyond the limits of todays technique: 0.01 arc seconds per pixel. The full image region of 7 arc seconds is usually disturbed within athmospheric szintillation effects and completely smoothed out in earth bound photographs.
Mzoom.001 (000d 03h:08m:23s): An image scale of 3.6 arc seconds across corresponds to 1600mm focal length.
Mzoom.0005 (000d 03h:29m:03s): Even at this near arc second scale (1.8") the fractal mountain / view ray intersection algorithm may detect exact intersections and sharp shadows. And it's even far away from the true limit...!
Mzoom.0002 (000d 03h:20m:47s): The sub arc second scale starts here, at 0.7 arc seconds along the image.
Mzoom.0001 (000d 03h:53m:49s): Just to note: The visible structures here are seen from a distance of 61km 471m, the small ridge of a size of mere 10cm, counting from the left side of the image to the right side.
Mzoom.00005 (000d 04h:08m:45s): The effective image size is 5.3cm or 0.18 arc seconds, beeing completely below the theoretical resolution limit of common small telescope.
Mzoom.00002 (000d 04h:16m:50s): In nature, one could expect to see flowers or other similar structures at an image size of 2cm across. But realistically not from a distance of 61km...
Mzoom.00001 (000d 04h:17m:07s): The 1cm scale. One pixel is 0.016 mm accross and one could expect to resolve microbes, if this were a somewhat more natural simulation. Just imagine a small, grinsing microbe sitting on top of every micropeak ;-)!
Mzoom.000005 (000d 04h:44m:53s): Trying to catch microbes? At 8.3µm per Pixel, this could become possible - and save for the observer, since the danger of infection can be considered very low from a distance of more than 60km.
Mzoom.000002 (000d 04h:31m:19s): Looking even further, deeply into the microbe's eye...
Mzoom.000001 (000d 04h:42m:08s): The 1mm scale. The true horizontal image size is just above 1mm.
Mzoom.0000005 (000d 04h:59m:06s): At these large zoom scales please also note the continously increasing rendering times due to the amount of fractal octaves which become visible. While the wide angle view took a mere 17 minutes, this zoomed image required 5h under same conditions.
Mzoom.0000002 (000d 05h:07m:13s): Even above the numerical limit: 0.2mm image size, 0.3µm pixel size. As 0.3µm are 300nm, details visible at this scale are of the order of the wavelength of visible light and would lead to diffraction effects in nature.
Mzoom.0000001 (000d 05h:26m:54s): Sharp details? In a *realistic* simulation, diffraction effects would overcome this monochromatic scenery with lots of colors. Normally, one would need a powerfull microscope to detect the details which are seen here from a distance of 61km.
Mzoom.00000005 (000d 05h:19m:04s): 53µm image scale, 83nm pixel resolution: The rock needle visible in this image could no more be seen by optical methods, one would need an electron microscope to verify its existince. But from a distance of 60km...?
Mzoom.00000002 (000d 05h:47m:24s): At last: The numerical limit. Each pixel is 40nm, and the intersection process comes into first troubles. Though not obvious in the image, some intersections are lost due to numerical instabilities. Nethertheless the absolute limit would be 10-10, about even 400 times smaller than this last image of this zoom serie. But due to unavoidable tolerances, this atomic size is beyond the useable limit. Just not note finally, that the useable limit already is far beyond the senseful limit...