Who hasn’t pondered the intriguing network formed by the interconnected veins of a leaf? Like many apparently complex self-organized structures, there is a recognizable pattern, but the basis of the pattern is difficult to grasp.
Remarkably, research published in 2002 (S. Bohn et al., Phys. Rev. E, June 2002.) found that there is a simple relationship governing the angles between vein segments in the leaves of dicotyledons, and that this relationship is universal. The study also found that the observed vein angles can be reproduced using a simple force model.
Numerical analysis of leaf scans revealed that the angles between vein segments are directly related to the thickness of the segments. When the vein sizes are similar, the connection appears to form a three-way junction with the angle between the veins about 120 degrees. If the vein sizes are dissimilar, with one much larger than the other, the smaller vein joins the larger at about a 90 degree angle.
The photograph is of a leaf of a Fremont cottonwood (Populus fremontii) along Las Virgenes Creek in Upper Las Virgenes Canyon Open Space Preserve. It was taken on a run from the Victory trailhead on May 16, 2007.
Runner on a track that connects Rocky Peak fire road to Las Llajas Canyon in Rocky Peak Park. From the top of this hill there is approximately 4 miles of fast downhill through a scenic canyon garnished with out of service oil wells and a gurgling creek.
A study of new growth on a California Bay Laurel (Umbellularia californica) at Sage Ranch that was burned and completely defoliated in the 2005 Topanga Fire. These are crown sprouts growing from the base of the tree.
A study of a Limber Pine cone on the summit plateau of Mt. Pinos (8831′). The photograph was taken on the Mt. Pinos – Lily Meadows – Mt. Abel run described in Thunderstorm.
Bright green highlights new growth on a Big Cone Douglas Fir (Pseudotsuga macrocarpa) in the San Gabriel Mountains near Josephine Peak and Strawberry Peak.
These peaks are popular lower elevation summits, that can be snow-free in Winter, or a blast furnace in Summer. Josephine Peak (5558 ft.) was once the site of fire lookout, and a fire road leads from Clear Creek Station to its summit. From the west, via Clear Creek or Colby Canyon, Strawberry Peak (6164 ft.) is a more difficult ascent that requires careful route-finding and rudimentary rock climbing skills. Many hikers prefer to do Strawberry from the east, starting at Red Box.
New sprouts of grass at Ahmanson Ranch less than a month after the Topanga wildfire burned 24,175 acres in the Simi Hills, northwest of Los Angeles. More photos and information regarding the Topanga Fire can be found in my Coyote Oak Journal article The Topanga Fire, Part I: Rain, Wind and Fire. (Photo from October 25, 2005.)
