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Geometries of Nature

Organic Matter

Geometries of Nature

May 2023

Curiosity drives everything we do here at Scan of the Month. The simple — but usually impossible to satisfy — desire to see inside of things has led to some unexpected CT scanning adventures over the last year and half. Our appreciation for complex engineering and thoughtful design has found us putting everything from a Sriracha bottle cap to a car airbag into our Neptune scanner. But human-made products aren’t the only things with impressive internal architecture.

This month, we turn to plants and examine a handful of the most beautiful and intricate botanical forms. Of course we could physically cut into any of these things, but slicing even the softest fig necessarily deforms it. Not only does industrial CT offer a nondestructive way to look within, it also lets us visualize subtle variations in density and quantify the mesmerizing patterns that make vegetables, fruits, and mushrooms so much more than food.

Engineered by nature, these delicate yet hearty organic structures constitute worlds unto themselves. Let the discovery begin.

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Italy, 2023

With its crown of perfectly-formed florets, Romanesco broccoli looks otherworldly — like an AI-generated vegetable. This bright green relative of broccoli and cauliflower is not only tasty with its nutty flavor, it’s also a ripe subject for scientists and mathematicians to research due to its fractal structure, golden ratio spirals, and compact growth pattern.

The structure of Romanesco broccoli is a classic example of a fractal pattern in nature. A fractal is a complex geometric shape that can be split into parts, each of which is a reduced-scale copy of the whole — a property known as self-similarity. If you zoom in on one of the buds, you'll see that it is made up of smaller buds arranged in the same pattern as the whole head. Zoom in again, and you'll see the pattern repeats itself. Our CT scans use hundreds of 2-dimensional X-ray images to create a 3D model. When we slice this 3D model and scrub up the Z-axis of the Romanesco, we see the fractal burst into fireworks.

Fractals aren’t the only feature of Romanesco that piques the interest of mathematicians. The number of spirals on any given head is also a Fibonacci number. The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones (0, 1, 1, 2, 3, 5, 8, 13, 21, etc.). Fibonacci numbers frequently appear in nature, often in structures that grow in a spiral, such as pinecones or sunflowers. If you count the number of spirals on a Romanesco broccoli in a clockwise direction and then in a counterclockwise direction, the two numbers you get will be consecutive Fibonacci numbers. Divide the larger number by the smaller one, and you’ll get a result close to the golden ratio (approximately 1.61803398875), another mathematical concept that frequently occurs in nature, art, and design.

But how does Romanesco produce these mesmerizing patterns? Our CT software can visualize its density variation with a range mapper, revealing denser areas toward the peak and down in the stem (in red), likely due to compacted cellular structures supporting the growth pattern. Surprisingly, the center appears less dense (yellow and blue), maybe because it serves as a nutrient reservoir for new buds and requires a more porous structure.

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California, 2023

Have you ever noticed that fig trees don’t flower? That’s because a fig isn’t (just) a fruit; it’s a sphere of inward-facing flowers, or syconium. Its existence hinges on a complex, codependent relationship with a specific wasp species. The female wasp enters the fig through a small hole, the ostiole, laying eggs and simultaneously pollinating the fig’s flowers. With our Neptune scanner, we can zero in on each stage in this fascinating example of symbiosis.

The female wasp’s journey begins as it makes its way into an unripe fig through the ostiole, a tiny hole at the bottom — barely visible to the naked eye. It’s a tight squeeze, and the wasp’s wings and antennae get ripped off as it travels through the ostiole, trapping it inside the fig for the complex reproductive dance that follows.

Once inside, the wasp lays its eggs within some of the fig’s flowers housed in the syconium, inadvertently pollinating other flowers in the process. The pollinator wasp dies soon after, and a powerful enzyme inside the fig digests its body.

The story comes full circle when the larvae hatch. Male wasps emerge first, fertilize the females that haven’t hatched yet, and then bore tiny escape tunnels into the fig’s wall. Having completed their task, they die. When the females hatch, they collect pollen from the now-mature flowers before escaping through their mates’ tunnels. They then take flight to find a new fig and begin the process all over again.

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California, 2023

The pomegranate, a symbol of abundance and prosperity, has evolved a structure that optimizes for seed dispersal via animals. The tough outer skin (pericarp) protects the seeds, while the juicy, sweet-tart pulp (arils) surrounding each seed attracts animals. When animals eat the fruit, they ingest the seeds, which can then be carried far from the parent plant and eventually excreted. This helps the pomegranate plant expand its range to new environments. CT scans reveal the keys to this evolutionary strategy — a study in maximizing space, natural compartmentalization, and layered protection.

Scrubbing upward along the Z-axis inside a pomegranate, our CT scan shows hundreds of seeds. Each seed is surrounded by a sac filled with juice, known as an aril. The aril is technically the seed coat, and it’s evolved to be delicious to animals.

The arils are neatly arranged in distinct compartments encased in bitter-tasting membranes, likely an evolutionary trait to safeguard and separate the clusters of seeds. The number of these chambers can vary, but it generally ranges from 8 to 15.

The pomegranate’s skin is tough and leathery, but only 1 to 2 mm thick, according to our CT scan. It’s composed of two layers: the outer pericarp, which provides protection and structure, and the inner mesocarp, which harbors the aril-holding compartments. This multi-layered casing offers an effective defense against both predators and environmental threats.

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Lion’s mane

California, 2023

Instead of the iconic cap-and-stem structure, lion’s mane mushrooms consist of white waterfalls of icicle-like spines. These long cascading tendrils hang from a single clump and grow on both living and dead hardwood trees, appearing in the late summer and fall. They’re prized in the culinary world for their seafood-like flavor, often compared to lobster or shrimp when cooked. Lion’s mane has also been attributed a wide array of health benefits, including enhancing cognitive function, reducing inflammation, and supporting overall neurological health. CT provides the perfect way to access the mysteries of this ephemeral and enigmatic fungus.

Mushrooms like the lion’s mane develop intricate networks of hyphae, their basic structural units. These hyphae form a web-like structure, known as a mycelium, that serves various functions, including nutrient absorption and distribution. This network extends far beyond the visible part of the mushroom, permeating the soil or wood substrate in which the mushroom grows.

The lighter color in this CT scan corresponds to higher density. These are the mushroom's tendrils or ‘teeth,’ where the hyphae are most tightly packed, providing structural support and efficient nutrient delivery. We can measure the teeth in our CT analysis software and find that on average, they extend about 4 mm out from the mycelium-rich fruiting body. And they’re surprisingly uniform; the tendrils in this mushroom are all roughly 0.4 mm in diameter.

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