The Wild Geometry Next Door

Lens-Artists Challenge #421: Exploring Geometry in Architecture, Nature, & Daily Life

Patti leads this week’s Lens-Artists Challenge. In her post, she asked us “to be a photo detective, hunting for geometry—circles, rectangles, squares, triangles, arches, spirals—on the street, or in nature, or in unexpected places.” I decided to stay with nature and see how artistic Mother Nature gets with geometric shapes.

Let’s begin with the Redstem Stork’s-Bill (Erodium cicutarium) flowers in my featured photo. I love the geometric arrangement of these flowers. The five petals form a pentagon, or a five-pointed star, with the orange-tipped stamens perfectly centered and rising. The flowers themselves rise from a single point at the top of the stem, like the spokes of a wheel, and the small oval green sections below them are buds that will open into more flowers. The geometry doesn’t end with the blooms. Once pollinated, each flower grows a long, pointed fruit, the “stork’s bill” that gives the plant its name. When it dries, each seed’s long tail (the awn) coils into a tight spiral. As the humidity rises and falls, that spiral twists and untwists, drilling the seed into the soil like a corkscrew. Leave it to Nature to come up with such perfection!

These two Common Buckeyes (Junonia coenia) caused a ruckus as they crossed right in front of my bike at SW Williamson County Regional Park this summer. They moved fast and seemed oblivious to everything. I didn’t know what was going on until I stopped and started chasing them with my camera. They were mating! OK, I get the urgency now. Look at their shapes. What I find beautiful about this image is that you get their triangular wings both open and closed in the same shot, the two butterflies joined tail to tail and facing opposite directions. Then there are the circles. Each eyespot is a set of concentric rings, like a target: a dark center, a paler ring, and an orange-and-black border. Scientists believe these eyespots work in two ways. The large, bold ones can startle a bird into backing off, while the smaller ones near the wing edges draw a peck away from the body, so the butterfly escapes with a torn wing instead of losing its life.

Speaking of mating, when two Familiar Bluets (Enallagma civile) mate, they form a beautiful heart-shaped loop called the wheel, or mating wheel. The male holds the female behind her head with the claspers at the tip of his abdomen, and she curls her abdomen forward to reach him near his thorax, closing the heart. The pair in my photo is in the tandem position, which comes just before and after the wheel. The bright blue male grips the olive-colored female behind her head, and together their bodies make one long line with a sharp bend where they connect, crossing the grass stem on a diagonal. Pairs often stay linked like this while they fly off to find a place to lay eggs. Look closely at the wings, too. Each one is a fine mesh of tiny four- and five-sided cells, like a stained-glass window in miniature.

Here’s a Mexican Primrose-Willow (Ludwigia octovalvis). I see hearts everywhere, from the small bud to the petal shapes. This flower is built on the number four. Four broad yellow petals form a cross, and four pointed green sepals peek out between them, turned at 45 degrees, so together they make an eight-pointed star. Also note the round center: a ball-shaped stigma sits inside a ring of eight stamens. Even the unopened bud above the flower, outlined in red, is angled like a little pyramid.

This is a Scrambling or Climbing Dayflower (Commelina diffusa). I got this macro in our courtyard just last week. The petals are only about ¼ inch (6 mm) long, so from our front door I can barely notice the flowers, and each one stays open for just part of a single day. While the leaves are lance-shaped to elliptic, the flower is built on threes, giving it a triangular shape: two large, rounded upper petals and a much smaller, cupped lower one. Look at the center, and you’ll find bright yellow structures shaped like tiny X’s. Those are staminodes, sterile stamens that help catch a pollinator’s eye, while the fertile stamens reach out on long, curving filaments.

I captured this final image two days ago while hiking in the beautiful Honey Creek State Natural Area. The public can enter the area only on guided hikes, and my master naturalist chapter organized one led by one of the park’s naturalists. This is a Texas Spiny Lizard (Sceloporus olivaceus). They can be hard to photograph because they don’t seem to enjoy human presence, but this one was clearly basking in its glory while a few of us photographed it. It blended in very well with the bark of the Ashe Juniper. Zoom in, and the geometry is in the scales. Each one is a keeled, roughly triangular plate ending in a sharp point, which is what gives the spiny lizard its name. They overlap like roof shingles in neat diagonal rows, and the dark bands across its back form wavy chevrons. Against the long, straight grooves of the juniper bark, it’s a meeting of two patterns: the lizard’s tiles and the tree’s parallel lines.

Looking back at these six images, I noticed something I hadn’t planned: Mother Nature likes to count. The dayflower is built on threes, the primrose-willow on fours, and the stork’s-bill on fives. The buckeyes add circles, the bluets lines and angles (and, a moment later, a heart), and the spiny lizard a whole mosaic of triangles. Few of these shapes are mere decoration. They guide pollinators to the flower’s center, fool a hungry bird, plant a seed, or keep a lizard hidden in plain sight. Patti asked us to be photo detectives, and the clues were never far away: a bike trail, a guided hike, and our own courtyard. Geometry, it turns out, is one of nature’s oldest tools.

Sofia’s wabi-sabi challenge last week showcased amazing photos from your collection. I hope you will join Patti’s challenge, too. Please don’t forget to use the “lens-artists” hashtag in your posts so people can find your wonderful challenge entries.

Next week, Beth will feature a new challenge. It will go live at noon EST in the USA. Tune in then to find out more about the challenge. Please see this page for more information about the Lens-Artists Challenge and its history. If you don’t want to miss any future challenges, please consider subscribing to the team members’ websites. Here they are:

• Tina of Travels and Trifles.
• Patti of P.A. Moed.
• Ann-Christine of Leya.
• John of Journeys with Johnbo.
• Anne of Slow Shutter Speed.
• Sofia of Photographias.
• Egídio of Through Brazilian Eyes.
• Ritva of Ritva Sillanmäki Photography.
• Beth of Wandering Dawgs.

That is the story behind the shots. For more like this, enjoy these related stories: Climbing Dayflower, Common buckeye, Familiar Bluet, Lens-Artists, Mexican Primrose-Willow, Redstem Stork’s-Bill, Scrambling Dayflower, Sunday Stills, Texas, Texas Spiny Lizard, Wildflowers, and Wildlife. Until the next shoot, keep chasing the light and the wonders it reveals.

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• Posted for Terri’s Sunday Stills Monthly Color Challenge: Leather Browns and Burgundy–Rich in Color, Rich in History.

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Sources

• Go Botany (Native Plant Trust) — Erodium cicutarium — https://gobotany.nativeplanttrust.org/species/Erodium/cicutarium/
• Gizmodo — This Seed Plants Itself by Corkscrewing into the Earth — https://gizmodo.com/this-seed-plants-itself-by-corkscrewing-into-the-earth-1693175430
• Kodandaramaiah et al., Deflective and Intimidating Eyespots: A Comparative Study of Eyespot Size and Position in Junonia Butterflies (PMC) — https://pmc.ncbi.nlm.nih.gov/articles/PMC3856750/
• Wikipedia — Familiar Bluet — https://en.wikipedia.org/wiki/Familiar_bluet
• Flora of North America — Ludwigia octovalvis — https://floranorthamerica.org/Ludwigia%20octovalvis
• Go Botany (Native Plant Trust) — Commelina diffusa — https://gobotany.nativeplanttrust.org/species/commelina/diffusa/
• Jim Conrad’s Backyard Nature — Commelina diffusa — https://backyardnature.net/q/diffusa.htm
• Rio Grande Valley Chapter, Texas Master Naturalist — Texas Spiny Lizard — https://rgvctmn.org/blog/texas-spiny-lizard/
• Texas Parks and Wildlife — Honey Creek State Natural Area — https://tpwd.texas.gov/state-parks/honey-creek