Amazing geodesic structures and architectural forms in the natural world

Posterior most end of Anurida granaria 100x photo enhanced

Posterior most end of Anurida granaria 100X photo enhanced. Angular illumination of the posterior most end of Anurida granaria highlights the geodesic nature of the cuticular layer in Springtails which consists of numerous protrusions which, like a corrugate matrix, give strength to the surface and prevent wetting of the cuticle by water or other fluids. Photo (c) 2001 by Terry Lynch.

Form the hexagonal honey cone made by bees to the spiral helix of DNA which is the basic code of all life forms, amazing geodesic structures and architectural forms pervade throughout the natural world. These often have been mirrored by man in the design of artificial tools, structures and other applications for it seems as if through the eons those most efficient and useful structures have already been worked out by species evolving and experimenting with designs to result in those most probably to insure survival of the species. Hence humanity may be wise to learn from nature and copy those designs proven over the millennium to work for bees, wasps, termites, Springtails and other small animals.

Recently I was sent some specimens of Springtails from a college in Christchurch, New Zealand. These were believed to be a variety of bioluminescent Collembola. I promptly examined the specimen under dark field illumination in hope of seeing its source of light and instead discovered for myself a spectacular mosaic of small conical impressions arrayed in a vast lattice over the tiny animals cuticle. What it was that I stumbled upon was the epicuticula ultra geodesic structure, a hexagonal layered lattice which serves to give form, strength and rigidity to the endoskeleton while at the same time serving as a base for the deposit of water repellant wax which enables this order of insects to float upon water. For simplicity sake, this structure will often be referred to as the GEO-structure.

Spectacular mosaic pattern of  Onychiurus sp. due to nature of cuticle as hexagontal lattice or GEO structure

Onychiurus sp. collected by Graham East and photographed using dark field illumination by Terry Lynch in August 2001. Photo (c) 2001 by Terry Lynch.

The epicuticula geodesic ultra structure is manifested to produce a mosaic pattern of tiny conical impressions, seen here under dark field illumination at 400X. This angular lighting makes visible what is invisible to the naked eye under regular perpendicular lighting of the subject.

Geo-structure modeled with corrugate at a perpendicular projection

Figure GEO1. Geo-structure of Collembola modeled at perpendicular projection. When a cardboard corrugate is photographed perpendicular to the surface the impression of a hexagonal structure is presented. This is very similar and analogous to the result one gets when using a scanning electron microscope to view the epicuticula ultrastructure of Collembola. An outstanding presentation of this fact is shown with the scanning electron micrographs presented as the"basic hexagonal epicuticular pattern" by Stephan Borénsztajn which are posted in the image gallery of the World Collembola site.

Geo-structure modeled with corrugate revealing nature of arced, curved or bowed surface which expresses its geodesic nature

Figure GEO2. Geo-structure modeled with corrugate revealing nature of arced, curved or bowed surface which expresses its geodesic nature. When the same surface shown in Figure GEO1 is observed from a distance it become apparent that this is a geodesic surface which is curved. In fact in this model the curvature was created by using a bow which expresses the concept that the surface presents strength to the structure such that there is a force which needs to be applied across the arc to maintain its rigidity. This is, in fact, one of the consequences of a geodesic surface in that when the arc is completed the entire surface remains under tension giving the organism its form and solidity.

Geo-structure modeled with corrugate has been rotated from the perpendicular projection

Figure GEO3. Geo-structure modeled with corrugate has been rotated from the perpendicular projection. Rotation of the geodesic structure begins to show how the impression of a hexagonal pattern comes into view.

The realization that the surface of the epicuticula of Collembola is geodesic in nature and not planar, that a projection of hexagonal 3D molecular structuring upon a curvature presents the most accurate and true description of this structure, is significant and noteworthy. This is demonstrated by a corrugate modeling of the Geo-structure as in Figure GEO1 where an arced or bowed corrugate rotated through a 90 degrees radial axes shows how a Geo-structure then appears when photographed and projected upon a flat surface of film. This indeed represents exactly what is seen when a SEM is used to observe and photograph the Geo-structure of Collembola. Should experts engaged in the research of Collembola then negate the geodesic nature of the epicuticula ultrastructure of Collembola or fail to emphasize this fact, they would be to failing to realize the true nature of this structure as geodesic in nature rather than hexagonal which implies a two dimensional plane.

Although this may be a matter of semantics more than a great realization, given certainly the scientific community has known for sometime a cuticle surface has thickness and layers, it is perhaps a terminology which warrants adoption by that community of Collembola experts if they want to most honestly and truthfully represent the nature of the cuticle which is geodesic for Collembola.

The spectacular structure presented by the cuticle of Springtails is but one example of how organisms have evolved to express the fundamental geometric design enabled by the genetic coding of all life forms. Other examples of this geodesic hexagonal architecture are seen in the compound eye of insects such as house flies, dragon flies, bees, wasp and ants.

One of the first human architects to recognize the structural advantages of the basic hexagonal lattice and employ this in construction of buildings was R. Buckminster Fuller. His impressive geodesic domes which utilize a framework of triangular or polygonal gridwork continue to inspire and impress sports fans and audiences who enjoy grand events presented under the canopy of great geodesic domes.

Although some might say these geodesic designs reflect the marvel and majesty of God's creation of the universe, I maintain that such designs are proof positive that the species have evolved. For what we see being expressed in the marvelous array of a Springtail's cuticle or an insect's compound eye is but a mathematical expression of that most fundamental and stable of forms, the triangle. All life based upon carbon will create such hexagonal patterns because the carbon atom is itself a four faced pyramid or tetrahedron and will bond with other molecules to produce a vast array of wonderful geometric crystalline structures. Perhaps the most noted of these is the diamond, carbon in its purest, most highly compressed form, that clearest of jewels we give to our dearest sweethearts and lovers!

Terry Lynch
13 January, 2002

Anurida granaria SEM imaged by Marcel Koken

Anurida granaria, A. granaria, bioluminescent, Springtails, Collembola, biolights, biolumin, project geo, setae trigger mechanism, TAL Glow Test
SEM of Anurida granaria, a tiny bioluminescent Springtail from New Zealand. SEM © 2016 by Marcel Koken. Digital image enhanced and colorized by Tal Lynch.

Marcel Koken SEM imaged Anurida granaria in February of 2016 from specimens collected by Graham East and fixed by Anthony Mitchell, both of South Island, New Zealand. The spectacular SEM images reveal in fine detail the waxy protective coating of Anurida granaria which repels water and other liquids. This protective waxy coating has remarkable structure which even prevents bacteria and other harmful microbe from sticking to the surface of Anurida granaria, hence serving as a barrier or shield and safe guard these awesome tiny creatures and contribute to their survival over the eons.

When imaged by photographing with darkfield illumination in 2001, the surface of Anurida granaria and other Collembola living in close association with them was observed to reflect that geometric structure laying beneath the wax layer. This is enabled as given when wax blossoms from the vertices of the lattice of hexagonal tubercles forming the cuticula, it forms larger structures which show up as a spectacular pattern when Anurida granaria and other Collembola are observed under darkfield illumination.

Anurida granaria, Frans Janssens, Terry Lynch, 3D modeling
Fig. 2016. Anurida granaria is shown (inset upper left corner) against a darkfield illumination photograph of its waxy surface layer. Circular insets C1 and C2 show 3D modeling of the surface coating at progressively larger magnifications that one may better understand how these structures give the appearance of a geometric pattern covering the surface of Anurida granaria and other Collembola. Photo and graphics 2016 by TAL. Tubercles 3D model by FJ.

Frans Janssens (FJ) made 3D models of these geometric structures, aka tubercles, giving permission to share them to help educate and inform everyone who is interested in Collembola and fascinated by every aspect of their tiny lives. In Fig. 2016, Anurida granaria (inset AG) was photographed with an optical microscope. Under darkfield illumination (background) the wax coating can be seen as a spectacular, gleaming surface of wax which hints of the a wondrous geometric lattice it is build upon. 3D modeling based on SEM images made by Frans Janssens were used to recreate the geometric patter (C1) which when magnified reveals the tubercles structure in more detail (C2). It is the nature of this 3D tubercles structure which provides a surface which is impervious to water and other potentially hazardous agents and organisms which protects Anurida granaria and other Collembola, enables them to float on water, to breath when submerged for long periods, or survive in an environment full of bacteria and other threatening organisms.

Thus Anurida granaria and other Collembola exhibit a cuticula which is quite spectacular, having a lattice of hexagonal tubercles which form protective ultrastructure. Indeed this is a most impressive geometric pattern, even when seen from afar via darkfield illumination. Yet when SEM imaged one is able to see just how spectacular is the lattice of hexagonal tubercles from which wax blossoms to create enlarged structures which form a protective barrier against the elements, to even protect Collembola from bacteria and other microbe. It is the nature of this spectacular coating and protective barrier which has enabled Collembola to survive and prosper through the eons, so wondrously designed that they have survived for hundreds of millions of years, perhaps proving unto all who discover the Collembola, that it is not always the fittest that survive; sometimes it is the tiniest and best structured creatures which survive.

Acknowledgements and Credits: Frans Janssens must be complimented for his excellent presentation which he has entitled, Some notes on the Ultrastructure of the Cuticula. Epicuticula. Review is made of the scientific literature and SEM images available as relates to the cuticula of Collembola.

23 Feb. 2016

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Copyright © 2001-2016 by Terry Lynch. All Rights Reserved. Background was produced by photo enhancement of a digital image of a corrugated structure used to model the hexagonal geometric epicuticula ultrastructure (aka geo-structure) of Collembola. In this definition "geo" refers to "geometric" or "geodesic" as the surface pattern of Collembola when seen from afar gives the impression of a geometric pattern. In fact, SEM imaging reveals that geometric pattern is the result of a lattice of hexagonal tubercles which at their vetices excrete wax which blossoms to form a protective layer barrier, aka the ultrastructure of the cuticula. Epicuticula.