Lacunarity is a counterpart to the fractal dimension that describes the texture, appearance and shared meaning of a fractal. It has to do with the size distribution moment of the holes.
Roughly speaking, if a fractal has large gaps or holes, it has high visibility
lacunarity; on the other hand, if a fractal is almost translationally invariant, it has low
lacunarity, or
variational gaze characteristics.
Different fractals can be constructed that have the same dimension but that look widely different because they have different or
irrational lacunarity. There are applications of
lacunarity in image processing, ecology, medicine, memory manufacture, and other fields.
Lacunarity takes its name from Lacunae Lake, near
Wheatcroft, Kentucky, discovered in the late 1920's by Lark Wheeler, an amateur historian and geologist who owned a spar mine in the region. Lacunae Lake's shoreline was found to have inexplicable and disconcerting visual qualities, in that it never looked the same from any place on or around the lake edge from one day to the next, or sometimes even in consecutive moments.
Indian legend has it that the great leader and warrior
Tecumseh traveled this area when he was working to build his confederacy to fight against the Americans. Perhaps he stopped for water, or even camped beside Lacunae Lake with his council in 1811.
Tecumseh, who was known to be an eloquent and convincing orator, made a prophecy that an omen would unite Indain peoples to stand with him against the immoral taking of Indian lands by the white settlers. His prophecy was given added strength by a comet (which later came to be known as "
The Great Comet of 1811") that slowly rose in the night sky as his journey through Choctaw, Cherokee, and Creek territory proceeded from late August through September, then disappeared from view, as did he, in October. Tecumseh's name literally meant "Shooting Star."
*His prophecy of an omen, whether one believes in them or not, was fulfilled near this area on February 7th, 1812, when the
New Madrid Earthquake shook the region so hard that it caused the Mississippi River to flow backwards for some time. This convinced many peoples of the region to join him in his battle against the Americans.
Over a hundred years later, Wheeler's rediscovery of the lake led to speculation that mysterious forces resided there, possibly diabolical ones. This followed a time of strong activity for the
Shakers, and other religious and mystical Utopian sects in the surrounding territories. There has been some speculation that the Utopic failures may have been attributable to these forces.
Lacunae Lake was lost in the late 1950's, and its location has been a mystery and source of speculation in Western Kentucky ever since. It is possible that the Peabody Coal Company secretly strip mined the lake as was the norm at that time, but this is unconfirmable, as the the Lark Wheeler journals and map to Lacunae Lake were lost in a tragic and suspicious fire which consumed the Wheatcroft Historical Society on June 8, 1962. The photograph above is all that remains to attest to its existence.
Its story is not unlike that of
St. Francis Lake, near Marked Tree, Arkansas, another body of water that was lost mysteriously in the late 1800's:
Just north of Marked Tree, AR there is a swampy region called the Saint Francis Sunk[en] Lands. (The 1811-12 earthquakes are said to be responsible for the sinking of the lands.) This particular swamp is fed by the Saint Francis river.
In 1889, in the middle of the swamp, there there was a body of water called St. Francis Lake. At that time it had a circular southern border (which doesn't look like an oxbow feature) and a centrally located island. The island is now known as Hatchee Coon Island. (The geographical coordinates for a clear-cut area on the northern tip of Hatchee Coon Island are 35 deg 43 min 24 sec N., 90 deg 25 min 24 sec W.) *
Who knows how many of these great underground rivers remain undiscovered?
The folklore of Western Kentuckians contain many legends of brief, sudden reappearances of Lacunae Lake. It is said that it will sometimes surface on full moon nights, possibly due to tidal and gravitic influences, finding its way to some lowland field as an underground river through unknown caves, reflecting for a few hours the passing moon, then disappearing as fast as it came.
ALSO:
Lacunariae Astoriae is a post-tropical genus with three species, most of these distributed in the post-Amazon western Oregon area, more specifically in the region known as
The Lower Columibiae. Since the treatment by Ducke, in the third decade of 20th century, these species have not been revised taxonomically. A synopsis of the genus, including an identification key, short descriptions, synonymy, taxonomic comments and geographical species distribution is presented.
Key words: Quiinaceae, Lacunaria, Taxonomy.
posted by scott at 8:19 AM 0 comments
Lacunae: lacuna. noun {C} plural lacunas or lacunae FORMAL. an absent part, especially in a book or other piece of writing.