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Patterned Chaos

Patterned Chaos

Simplicity piled upon simplicity creates complexity, reads a line in Matt Ridley’s book Genome. This complexity is often mistaken as chaos in wild nature, but a closer look, however, reveals repeating geometric patterns in virtually every minute structure, at virtually every scale. Such patterns were termed as fractals in 1975 by mathematician Benoit Mandelbrot, who applied elegant and simple sets of numbers and equations to explain their beauty. Here, we ‘apply’ imagery from nature to share with readers the magic of fractals, whose design is wholly determined by function.

Compound Eye of a Fly

Photo: Purva Variyar.

When observed under a scanning electron microscope (SEM) and magnified over 300 times, this compound eye of an unidentified fly reveals a stunning fractal pattern in a falsely-coloured photomicrograph. The microscopic polygons are individual visual receptor-units or ‘eyes’ called ommatidia, which come together in perfect symmetry to form a powerful compound eye.

Andaman redwood seed

Photo: Kalyan Varma.

The branched veins on the leaf-like seed of an Andaman redwood tree Pterocarpus dalbergioides possessively protect the seed spore in its clasp resulting in this impressively-patterned armour! Visitors to the Andaman and Nicobar Archipelago are able to spot these trees at the famous Cinque Island, south of the Rutland Island.

Vein Skeleton of a Leaf

Photo: Bhavya Joshi.

The softer tissues of a Ficus religiosa leaf have decomposed leaving behind this skeleton depicting a striking, reticulate-venation design with repeating units clearly visible when magnified. This branched system once served as part of the nutrient and water transport system of the leaf.

Snake scales

Photo: Tasneem Khan.

This is a close up of the geometric arrangement of scales or scutes on the body of an Andaman bronzeback. Ruthlessly functional, the scales are made from keratin and have a multi-pronged utility – they help retain moisture, aid in locomotion, provide grip and friction, help in camouflage and enable anti-predator display.

Spider web

Photo: Bhavya Joshi.

Every micrometre of spider silk is vital to the web structure, which is both, a work of art and a precision-engineering feat. Tougher than steel of the same weight and girth, even stronger than Kevlar, the web is strengthened when amplified by its assigned geometry. In this case, the web was woven by a signature spider and is embellished with glistening, perfectly-shaped dew drops that are themselves composed of fractal patterns.

Fern leaf and spores

Photo: Kalyan Varma.

There is beauty in symmetry. The neat, geometrical arrangement of the sporangia or spore sacs on the undersides of the compound ‘leaves’ of the fern and the ‘leaflets’ is as impressive as it is functional. The appropriate term for leaves in ferns, is fronds.

Whirligig Beetles

Photo: Manav Joshi.

This arresting mass of tiny, metallic-black bodies floating in a stream is a collective of whirligig beetles. These insects, perfectly adapted to aquatic life, have legs modified for swimming, and possess a pair of bisected compound eyes that enable the creatures to see above and under water simultaneously. What is more, they carry with them a nature-crafted scuba tank – an air bubble on their abdomens that allows them to stay submerged for relatively extended periods of time!

Giant Rusty Millipede

Photo: Arvind Ramamurthy.

The perfect spiral of the coiled body of this giant rusty millipede bears a likeness to the ‘Golden Spiral’, which conforms to the famous Golden Ratio, a universally-accepted mathematical measure of beauty and aesthetics routinely found in nature. Even the identical, repeating body segments and seemingly infinite number of legs add to its fractal charm.

Brain Coral

Photo: Tasneem Khan.

Maze-like grooves known as ‘valleys’ run through an entire coral colony. Members of the brain coral family bear a striking resemblance to the anatomy of our own brains, and when you explore the polyps connected to each other by their exoskeletons the consistent pattern becomes evident.

Elephant Trunk

Photo: Kalyan Varma.

Even the discoloured skin texture of an elephant’s trunk exhibits intricate lines and crevices that is all the more impressive when examined closely. Within the self-repeating pattern, the melanin-rich patches enhance the apparent chaos using fractal designs, visible only to those who carefully look for them.

Peacock Plumage

Photo: Nishant Patel.

This iridescent, characteristic blue-green metallic shimmer of peacock feathers is created by the physics of light, not the chemistry of pigments. Even without the characteristic spread of feathers, when closed, each feather reveals an elegant fractal pattern of its own.

Water-made structures

Photo: Saee Bhurke.

The ebb and flow of the rivers leave behind distinct signs, and from these, unique patterns emerge. Along the edges of the part of the river basin of the 182 km.-long Tsarap river in Ladakh, water has eroded the land in a manner a sculptor might carve out a handsome, giant structure. Of course, wind and rain pitched in to accentuate the elegant designs.

Forest Fractals

Photo: Saurabh Sawant.

If you go out to look for them, fractals will materialise everywhere. Here we see an aerial view of an alpine forest. These conifers in Arunachal Pradesh grow to around 30 m., and as can be seen they display a striking symmetry when seen from afar. Under their canopy, of course, virtually every leaf, bark, seed and stone possesses its own unique symmetry, adding allure and mystique to forests that inspire poets to poetry, artists to art and scientists to enquiry.

First appeared in: Sanctuary Asia, Vol. XXXVII No. 2, February 2017.

 
 
 

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Ganesh R Mandavkar

February 11, 2017, 03:30 PM
 Beautiful