Patterns in nature
at La Saladita.

Counting the side plates

Down each side of the shell, between the center row and the rim, green (black) turtles and hawksbills have four large plates, and the two sides normally match. The olive ridley, the turtle that nests most here, does not have a fixed number: usually six to eight pairs, sometimes as few as five or as many as ten, and often a different count on the left and right. In 655 olive ridley hatchlings from Sri Lanka, researchers found 120 different shell layouts, and about 61% were symmetric. The rim plates hardly varied: 92.7% had 13 pairs.

See it yourself: In a clear photo of an olive ridley's back, count the side plates on the left and on the right. Often they won't match.

Plates that overlap like roof shingles

On most hawksbills each shell plate overlaps the one behind it like a roof shingle, and the back edge of the shell is jagged like a saw. Hatchlings and some adults lack the overlap. Young olive ridleys also have slightly overlapping plates with small keels, but adult ridley plates sit edge to edge.

The leatherback: a mosaic instead of plates

The leatherback has no hard plates at all. Under its skin is a layer of thousands of small, irregular, interlocking bones that start growing along the ridges about seven months after hatching and spread until they cover the back. The back has five lengthwise ridges, seven if you count the two side edges. Hatchlings are covered all over in tiny, soft, many-sided scales that are gone within the first weeks.

Leatherback ridges shape the water flow

A computer flow study found that the leatherback's back ridges sit at a slight angle to the water flowing past. That angle makes small swirls that keep the water attached to the shell longer, which improves swimming. This was a simulation, not a measurement on live turtles.

Two tilings stacked and offset

A hard sea turtle shell has two layers: bone underneath and keratin plates on top. The seams between the plates do not line up with the joints between the bones, a bit like a brick wall where each course is offset from the one below.

How the plate pattern forms: two published models

Each shell plate starts in the embryo as a small thickened spot in the skin, called a placode. A reaction-diffusion model, the family of math Alan Turing proposed for animal patterns, can reproduce both the normal plate layout and the odd variants seen in real turtles; a 2023 paper still calls this a hypothesis. A second model ties each plate to the embryo's repeating body segments, and it was tested on olive ridleys: their 120 layouts all fell inside what the segment model allows.

Odd plate patterns: nest heat, and family

Extra, missing or split plates showed up more often when sea turtle eggs incubated hot, and more so when the sand was also dry. But in olive ridleys the clutch a hatchling came from mattered, which points to the parents' genetics too, so the cause is not settled. Turtles keep their odd layout as they grow. The basic plate layout of turtles has stayed the same since the Early Jurassic.

Growth rings show growth, not birthdays

A shell plate grows by adding material around its edges and by thickening, which can leave ring-like lines. A review of 145 studies found that counting them gives age only where the count has been calibrated for that population. When researchers dated hawksbill plate layers in Hawaii, the turtles laid down about eight lines a year, not one. Scientists age olive ridleys from growth layers in the upper arm bone instead; in the North Pacific that put maturity at about 13 years. Both local wood turtles have shells made rough by growth rings.

Eye-spots, rays and streaks

Each side plate of the ornate slider usually carries an eye-spot, which can fade or darken with age: a yellow-orange ring around a dark center, so the shell has a row of eyes down each side. The painted wood turtle's side plates range from plain to a single spot, lines or eye-spots, and its center plates may have rays fanning out. Hawksbill plates are streaked and mottled in amber, brown and black. Young green turtles elsewhere have radiating streaks, but the local black turtle is usually dark, plain or spotted. Nobody has published how the slider's eye-spots form.

See it yourself: Sliders bask on logs in the lagoon. With binoculars, from well back, look for the row of eye-spots. Crocodiles live in the lagoon: never stand at the edge after dark and never wade.

A face like a fingerprint

The many-sided scales on a sea turtle's cheek work like a fingerprint and stay the same from hatchling to adult; after decades of photo-ID, no two turtles have been found with matching faces in clear photos. Researchers identify individual green turtles, hawksbills and olive ridleys from side-of-head photos, and the left and right cheeks differ, so both sides are photographed. Hawksbills have fewer facial scales and are harder to tell apart. Leatherbacks have no facial scales as adults. Head scales also tell the species apart: green and black turtles have one pair of large scales between the eyes, hawksbills and olive ridleys two.

Mirror tracks and zigzag tracks

Leatherbacks and green (black) turtles crawl by pulling with both front flippers at once, which leaves a track whose left and right halves are near mirror images. Olive ridleys and hawksbills move their front flippers one after the other, which leaves staggered, zigzag marks. Olive ridley tracks are about 70–80 cm wide, black turtle tracks 70–90 cm, leatherback tracks 150–230 cm.

See it yourself: Early on nesting-season mornings, look at fresh tracks from the water to the dune, from the side. Zigzag marks 70–80 cm wide are most likely an olive ridley, the commonest nester here. Don't step on tracks, dig, or approach a nesting turtle, and leave marked nests alone.

The mud turtle's three keels and two hinges

The Mexican mud turtle's upper shell usually has three low lengthwise ridges, clearest toward the back. Its lower shell has two hinges across it, one in front of and one behind the middle plates. The species' reference specimen is officially from Acapulco, Guerrero. The mud turtle in this site's field log is a provisional ID from a top view, so its hinges were not seen.

A tipping point in the nest

Nest temperature in the middle of incubation decides whether olive ridley hatchlings become male or female. At a nesting beach in Costa Rica, the 50:50 point was 31.5 °C, with the switch happening between about 30.6 and 32.5 °C, the highest pivot recorded for any sea turtle. That number comes from Costa Rica and should not be applied to nests here.

Barrel cactus ribs in Fibonacci numbers

In a related barrel cactus, 49% of plants had 13 ribs, 42% had 8 and 7% had 5: all Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21…), each the sum of the two before. An earlier study reported the same in 15 other Ferocactus species. Nobody has published a rib count for the local Ferocactus lindsayi.

See it yourself: Count the ribs at the top of a mature barrel cactus. A count that isn't a Fibonacci number is real data too.

Crossing spirals on a pincushion cactus

The bumps on a Mammillaria form two sets of spirals, one winding left and one right. In a measured species the counts were 8 and 13, two consecutive Fibonacci numbers, and in another the placement of each new bump fit the golden angle, about 137.5°. The local Mammillaria beneckei has not been counted.

See it yourself: From above, follow one bump to its nearest neighbors in a gentle curve to the center. Count the curves going clockwise, then counterclockwise.

The golden angle on a nopal pad

The spine cushions on a pad sit in crossing diagonal rows. In a measured Opuntia, the golden angle (about 137.5°, the turn between one cushion and the next) described their placement best. A 2019 modeling study found that other Fibonacci-type angles capture light just as well, so the popular idea that the golden angle is uniquely best for sunlight is not supported.

See it yourself: Lay a ruler along a diagonal row of spine cushions on a flat pad, then find the row that crosses it.

Organ-pipe cactus ribs are often not Fibonacci

Tall columnar cacti have straight vertical ribs. In the one large count, of a related Mexican columnar cactus, many plants had 12, 13, 14 or 15 ribs, so many counts were not Fibonacci numbers. The seedlings started out with a Fibonacci spiral and only later switched to straight ribs.

See it yourself: Count ribs on several pitayo stems at the same height and compare.

Rosettes and leaf prints

Agave leaves grow in a tight rosette. While packed in the central bud, each leaf presses on its neighbors and keeps their outline as pale "bud-prints". Most bromeliads also set their leaves in a spiral rosette, and some Tillandsia set them in two opposite rows instead. No published Fibonacci count exists for any agave or bromeliad here.

See it yourself: Look for faint copies of a neighboring leaf's edge and teeth pressed into an agave leaf.

Left-handed and right-handed coconut palms

The leaves on a coconut palm climb the trunk in either a clockwise or a counterclockwise spiral. Crosses produce both kinds in about equal numbers, so the direction is not inherited. Claims that the direction follows latitude or the Earth's magnetic field are contested.

See it yourself: Stand under a palm, follow the old leaf scars upward, and note which way they climb. Neighboring palms can differ.

Valley folds and roof folds in palm leaves

Palm leaves start out pleated like a folded fan. In the palmetto (Sabal) the folds make a V that holds rain. In the coconut they make an upside-down V that sheds it.

See it yourself: Look at a leaflet's cross-section: on a palmetto it is a valley, on a coconut a roof.

The five-pointed star in a morning glory

Morning glory flowers are built in fives. In bud the flower folds into five pleated panels with five exposed bands between them, and those bands show as a five-pointed star on the open flower.

See it yourself: Look straight into a beach morning glory on the dune.

Most climbing vines twist the same way

Across 17 sites on both sides of the equator, 92% of 1,485 twining stems wound into a right-handed helix, and the share did not change with latitude or hemisphere. The direction of the local species was not measured.

See it yourself: Look down on a vine wrapped around a fence wire and trace which way it turns as it climbs.

Passionflowers: fives with a three in the middle

Passionflowers have 5 sepals, 5 petals and 5 stamens, but 3 styles, so a five-fold and a three-fold pattern share one center. One or more rings of thread-like filaments sit between the petals and the stamens.

See it yourself: Count the stamens (5), then the club-shaped styles above them (3).

Pinwheel flowers: fixed in frangipani, mixed in hibiscus

Frangipani petals overlap like a pinwheel, and in this genus the overlap turns the same way in every flower, so botanists use it to identify the genus. Hibiscus petals also overlap like a pinwheel, but on one plant some flowers turn one way and some the other, roughly half and half; that last part rests on a review, not the original study.

See it yourself: Compare several frangipani flowers from the front: every one turns the same way. Then tally ten hibiscus flowers on one bush.

A tendril that changes hands

Once a tendril grabs a support, both its ends are held, so it can only coil by making a left-handed coil and a right-handed coil joined by a short straight piece, which Darwin called a "perversion". Pulled, it winds tighter instead of unwinding. This was studied in cucumber, the same genus as the local melon.

See it yourself: Find a tendril attached at its tip. Somewhere along it the coil reverses.

The exploding haba fruit

Ripe haba (habillo) fruits burst and throw their flat seeds; a 2015 study on the Costa Grande of Guerrero describes it. In its close relative, the sandbox tree, seeds left at an average 43 m/s at an average 34° above horizontal, close to the best angle for distance, spinning fast and flying with backspin, which lowers drag.

See it yourself: Look under a fruiting tree for wedge-shaped fruit segments and flat seeds scattered far from the trunk. Don't stand under it when the fruit is ripe.

Kapok and pochote: fives

Ceiba flowers have five petals, and the woody pod splits along five seams, occasionally six, to release seeds in silky fiber.

See it yourself: Count the seams on an opened pod.

Dayflowers and spiderworts: built in threes

These flowers have 3 sepals and usually 3 petals. Dayflowers look two-petaled because the third petal is small and pale.

See it yourself: Compare a Tradescantia flower (three equal petals) with a dayflower (two large blue petals and one small).

Mangrove props are branches that branch again

The arching "stilt roots" of the red mangrove are leafless branches that grow down to the mud, branching again and again before they root. Nobody has measured them as a fractal, so the site doesn't call them one. In a related black mangrove, many thin roots and a few thick ones added up to about the same total cross-section in each size class, as a "pipe model" predicts; the local black mangrove was not measured.

See it yourself: From a boat or the bank in daylight, follow one prop from the trunk down: it forks, and each fork arches and forks again. Keep back from the water; crocodiles live in the lagoon.

Leonardo's rule for branches

Leonardo da Vinci noticed that when a branch splits, the combined cross-section of the two new branches about equals the parent's. A 2011 physics paper argues this follows from trees building self-similar skeletons sized to resist wind. It has not been measured on local trees.

Leaf veins form loops

The most efficient way to deliver fluid would be a branching network with no loops, yet broad leaves are full of closed loops. That lets water route around a damaged vein, and models show loops become the best design once damage is included.

See it yourself: Hold a sea-grape leaf to the light and follow fine veins until they meet and close a loop.

Fern fiddleheads

A new fern leaf comes up tightly coiled because its underside grows faster at first, and it unrolls when the upper side catches up. No source shows this coil is a logarithmic spiral, so the site doesn't call it one.

See it yourself: Look for coiled new leaves at the center of a leather fern clump at the mangrove edge.

Seed-head spirals in the sunflower family

In sunflower seed heads, the counts of clockwise and counterclockwise spirals are usually, but not always, Fibonacci numbers: a large citizen-science study found 565 of 768 counts were. It also reported heads with no Fibonacci structure at all. The local relatives (red sunflower, zinnia, cempasúchil) have not been counted.

See it yourself: On a large, fully developed Tithonia head, try counting seed spirals in each direction.

Fairy rings

The green-spored parasol grows outward underground from a starting point. As it uses up food in the middle, the mushrooms come up in a widening circle. This mushroom is a common cause of mushroom poisoning: do not eat it.

See it yourself: After rain on lawns, look for a circle or arc of large white parasols, sometimes with a ring of darker grass.

Rings on caps and under them

Most mushrooms have gills that radiate like wheel spokes, but in Coltricia montagnei the underside breaks into rings around the stem, like a target. Turkey tail lays down concentric bands of color as it grows outward. The artist's conk lives for years and adds a fresh layer of spore tubes roughly each year, so a cut conk shows stacked layers.

See it yourself: Turn a Coltricia over: rings, not spokes. Don't cut living conks on park trees.

Gill spacing set by spore physics

A spore is flung a tiny distance off the gill by a water droplet and must fall clear before hitting the next gill. A 2021 model and measurements suggest gills are spaced just far enough apart to pack the most spores into the least tissue; the authors predict gill spacing scales with spore radius to the 3/2 power.

See it yourself: Under a cap, full-length gills alternate with shorter ones that fill the wider gaps near the edge.

Earthstars and pinwheels

The earthstar's outer skin splits and peels back into a star of 4 to 9 arms around a round spore sac, so it has no fixed symmetry number. The tiny orange pinwheel mushroom has a cap folded into radial pleats like a paper umbrella, with a few widely spaced gills underneath.

See it yourself: Count the arms on several earthstars and note how much the count varies.

Snail shells: the logarithmic spiral

A snail adds shell at the opening and keeps the same shape as it grows, so each turn is a scaled-up copy of the last, close to a logarithmic spiral; the ratio between turns is approximately, not exactly, constant. In cone shells each new turn almost covers the last, so the spiral shows mainly on the flat top.

See it yourself: Look down on the flat top of an empty cone or murex shell and follow the spiral from the tip outward. Cone snails sting with a venomous harpoon: never pick up a cone with an animal inside.

A cone shell's pattern is a timeline

A cone shell's pattern is laid down one line at a time along the growing lip, so the shell records the pattern over time. A math model of how the mantle switches pigment on and off was fitted to 19 cone species and reproduced their patterns; none of the three local cones was among them. More generally, shell patterns are a classic test case for reaction-diffusion, where a substance boosts itself nearby and is held back farther away.

See it yourself: On an empty cone shell, the lines and blotches run across the growth lines; each growth line is one step in time.

Puffer mazes from mixed spots

A reaction-diffusion (Turing) model predicts that crossing a light-spotted puffer with a dark-spotted one gives a maze-like pattern in between, and genome data showed that maze-patterned Arothron species arose from such crosses. Nine Arothron species were measured; the two local puffers were not among those named.

See it yourself: Snorkeling the rocky points, compare the white-on-dark spots of the two local puffers. Don't provoke them to inflate; puffers are toxic to eat.

The boxfish's hexagon armor

The spotted boxfish's body is a box of bony plates. Most plates touch six neighbors, like a honeycomb, and five- and seven-sided plates fill in where the surface curves, the same reason a soccer ball needs pentagons. This species was one of 13 boxfish scanned in 3D for the study.

See it yourself: On a spotted boxfish, or a good photo of one, the white dots sit on a faint grid of six-sided plates.

A seahorse tail is square

Most animal tails are round, but a seahorse tail is a square prism, built from ring-like segments of four L-shaped bony plates. 3D-printed models showed the square version resists crushing better and keeps its joints lined up when bent and twisted. The specimens studied were two other seahorse species, not the giant seahorse found here.

See it yourself: If you see a giant seahorse holding a rope or mangrove root, look at the tail's flat sides. Don't handle it.

Whale shark spots read like star maps

Each whale shark's white spots form a unique layout. Researchers adapted software written to match star fields in telescope images, treating the spots like stars and comparing the triangles they form; it matched known pairs in more than 90% of tests. This is a tool for reading the pattern, not an explanation of how it forms.

See it yourself: Never touch or chase a whale shark. A side-on photo behind the gills is what ID libraries use.

Sea stars: fives with one odd spot

Most adult sea stars are built in fives: five arms, five grooves of tube feet. The symmetry is not perfect: a small sieve plate on top, the madreporite, sits between two arms and marks one direction. Their larvae are bilateral, with a left and a right side, and the five-part adult forms at metamorphosis. A brittle star has five identical arms but walks with a temporary front: it picks one arm to lead and moves the arms on either side in mirror-image pairs (shown in a Caribbean species of the same genus).

See it yourself: Count the arms on a sea star in a tide pool, then find the small light dot on top between two arms. Look without lifting it.

The urchin shell: 20 columns in fives

A regular sea urchin's shell is made of 20 rows of plates: five bands with pores for tube feet alternate with five bands without, each band two plates wide. Its jaw, called Aristotle's lantern, works five teeth.

See it yourself: On a sun-bleached empty urchin shell on the beach, find the five double bands of tiny pore pairs and the five-pointed mouth underneath. Don't touch live urchins; the spines break off in skin.

Sea anemones: sixes with a hidden left and right

Sea anemones look round from above, but their internal partitions are laid down in pairs to make a six-pair plan, with a hidden bilateral axis through two special pairs. Group-level result; the local species were not checked.

See it yourself: Look straight down into an open anemone in a tide pool. Don't poke it.

Blue button: rings, rims and areas

The blue button's float is a disc of gas chambers in concentric rings, with new rings added at the edge, a bit like tree rings. Its tentacle polyps form only along the rim, so their number follows the circumference, while its reproductive polyps form across the face, so theirs follows the area.

See it yourself: When blue buttons wash up, look at the golden-brown disc from above for the rings. Look, don't touch: it stings, though far less than a man-o'-war.

Left-handed and right-handed man-o'-war

A man-o'-war colony is built asymmetrically: its first tentacle and later buds go to one side, giving mirror-image left- and right-handed colonies. The popular idea that one hemisphere has more left-handed ones has no supporting evidence. Shown in the Atlantic species of the same genus.

See it yourself: Photograph stranded ones from above and compare which side the main tentacle hangs from. Never touch: stranded man-o'-war still sting.

Chitons: always eight plates

Chitons carry a row of eight overlapping plates instead of one shell, which lets them bend to fit rough rock and curl up.

See it yourself: Count the plates on a chiton clamped to a rock in the splash zone. Don't pry it off.

Left-clawed hermit crabs and cone-shaped homes

Hermit crabs have one larger claw used to close the shell opening, and in the family of the local red-leg hermit crab it is usually the left. A Mexican Pacific study of this species found that larger crabs shift to preferring cone-shaped shells, and cone-shaped shells gain weight faster, relative to the room inside, than rounder shells.

See it yourself: In tide pools, see which claw is bigger on a red-leg hermit crab and what shells the big ones carry. Leave them in place.

Humpback song is built like language

Male humpbacks sing a song for 7 to 30 minutes and then repeat it with considerable precision. Songs are nested: units inside phrases, phrases inside themes, themes in a fixed order. A 2025 study found the song's parts follow a power-law frequency pattern like word frequencies in human language. Songs have been recorded in Mexico. The upward spiral bubble nets humpbacks use to feed are made on summer feeding grounds up north, not here.

See it yourself: In winter, a hydrophone dropped from a boat offshore may pick up singing. Keep the legal distance from whales.

Spotted dolphins gain spots with age

Pantropical spotted dolphins have no spots at birth and accumulate them as they age until they are almost completely covered. It is a documented pattern, though nobody has modeled it mathematically.

See it yourself: In photos of a passing pod, compare the plain gray young with heavily spotted adults.

Why honeycomb is hexagons

Among all ways to divide a flat surface into cells of equal area, regular hexagons use the least total wall. Thomas Hales proved it (published 2001). For bees, less wall means less wax, which is the usual reading of the theorem rather than something tested on bees. How bees actually make the hexagons is still debated: one group says warm wax flows into shape on its own, another filmed bees shaping the walls directly.

See it yourself: Look at comb only in a managed hive. Honeybees here may be Africanized: don't approach wild colonies.

The waggle dance: an angle on the comb is an angle in the sky

A dancing honeybee runs straight across the vertical comb at an angle from straight up. That angle equals the angle between the sun and the food, and the waggle run lasts longer the farther away the food is.

Paper wasp nests: hexagons with defects

Paper wasp nests are open combs of six-sided cells. In a measured Asian species the hexagons lined up in the same direction across the whole nest, but the grid was not perfect: some nests had paired 5-sided and 7-sided cells where the grid adjusts. The local species were not measured.

See it yourself: Look at an abandoned nest on the eaves in the dry season. Stay away from active nests; the executioner wasp's sting is very painful.

Orb webs: spokes and a spiral that isn't textbook

An orb web is a set of straight spokes with a sticky line wound around them. Across many species the gaps between sticky turns are about twice as wide near the edge as further in, and the spokes spread 4 to 5 times farther apart at the edge, so the spiral is neither a true Archimedean spiral (equal gaps) nor a logarithmic one. In almost all vertical orb webs the hub sits above the middle, leaving more catching area below.

See it yourself: Early morning dew makes the spiral visible. Look and photograph; don't touch.

The golden silk spider's off-center web

This spider puts the hub near the top, so most of the catching area is below. In a small experiment on the International Space Station, with two spiders, webs built without gravity came out mostly symmetric. Unlike most orb weavers, its sticky-spiral gaps don't widen toward the edge.

See it yourself: Large golden webs in shaded scrub. Watch without touching.

The silver garden spider's X

The silver garden orbweaver often adds bright zigzag silk bands in a cross through the hub. Its purpose is still argued: it decorated more where stingless bees, its main prey, were common, but heavy decorators survived less well.

See it yourself: Look for the white X at the web center in sunny gardens. Look only.

Army ants run three-lane traffic

On busy raid trails, ants heading out walk along both edges and ants carrying prey home use the middle. A math model shows the three lanes come from a small difference in how sharply the two groups turn to avoid each other, and the lanes cut head-on collisions.

See it yourself: If a raid crosses a path, step aside and watch from a meter away. They sting.

Leafcutter trails branch at a trade-off angle

Where leafcutter trails split, the angle is a compromise: a sharp angle shortens the walk, a wider one means less new trail to clear. Colonies in open ground used sharper branches; colonies in forest, with more litter to clear, used wider ones. Shown in other Atta species, not the local chicatana.

See it yourself: Watch cleared trails near big nest mounds from the side. Don't dig into nests.

The gold beetle that turns red

A golden tortoise beetle's gold is not pigment. It comes from stacked thin layers kept moist; light reflecting off each layer adds up to gold. When disturbed, the beetle drains the layers, the reflector stops working, and the red underneath shows. Shown in a Panama species of the same genus.

See it yourself: Look on morning glory leaves. Watch; don't poke it to make it change.

Hexagons in an insect's eye

An insect's compound eye is built from many small units packed as hexagons. A physics model of fruit-fly eyes shows that when unit size varies, the hexagon grid gains defects.

See it yourself: Take a macro photo of a perched dragonfly's eye.

The butterfly wing ground plan

Many butterflies in this family share one basic layout of bands and spots that mirror each other across central lines, with a row of eyespots near the edge. In the buckeye genus, removing or moving the center of a future eyespot erases it or makes a new one, so each eyespot grows outward from a central point (shown in a buckeye of the same genus as the local mangrove buckeye).

See it yourself: Photograph a buckeye with open wings at the mangrove edge.

The monarch's sun compass

Migrating monarchs steer by the sun and correct for its movement across the sky using an internal clock. Shifting their clocks by 6 hours shifted their heading in a predictable way.

Crocodile face scales form like cracks

Most reptile scales are laid out by a genetic and chemical patterning process. The scales on a crocodile's face and jaws instead form like cracks in drying mud: the growing skull stretches very stiff skin, and it splits into random polygons, so the left and right sides don't match. This was measured in Nile crocodiles; the American crocodile in the lagoon has not been examined.

See it yourself: Only from a boat or bank at a long distance, or with a zoom lens. Never approach, feed or wade near crocodiles.

Armadillo armor of hexagonal tiles

The armadillo's shoulder and hip shields are a mosaic of small hexagonal bone tiles tied together by flexible fibers. The bands in the middle use overlapping rectangular tiles so the animal can bend.

See it yourself: At night, from a distance. Don't handle armadillos; they can carry leprosy bacteria.

Running on water

A basilisk stays up by slapping each foot down hard and pushing back before the air pocket around the foot closes. Most support comes in the first half of each step, plus large sideways forces that keep it from tipping. Measured in a related basilisk.

See it yourself: At stream and lagoon edges they run when startled. Don't chase them.

Pelicans surf the air over the wave

Brown pelicans gliding just above the water get lift from the air pushed up ahead of a moving swell. A physics model estimates that flying low over the water saves about 15–25% of the energy of moving, and following the wave's slope can cut much of what remains. These are model estimates, not measurements. In a related pelican trained to fly in a V, birds had lower heart rates than flying alone.

See it yourself: From the beach, watch lines of pelicans skimming the face of incoming sets.

Frigatebirds: spiral up, glide down

Frigatebirds barely flap. They circle up in rising warm air under clouds, then glide long distances to the next lift; tracked great frigatebirds in the Indian Ocean stayed aloft for months this way.

See it yourself: On hot afternoons, look up for frigatebirds circling over the point with no wingbeats.

Hummingbird shine is layered light

A hummingbird's flashing colors come from stacked, flat, air-filled melanin plates in the feathers, not from pigment color alone. Light reflecting off each layer adds up, so the color changes with the viewing angle.

See it yourself: Watch a hummingbird turn at a flower: the throat flashes and goes dark.

Spotted cats and Turing's math

A model of two interacting chemicals produces spots and then rosettes like leopard and jaguar coats, and gene work in domestic cat embryos found a striped pre-pattern laid down before fur grows. Neither the ocelot nor the margay has been studied.

See it yourself: Camera-trap photos only; both cats are rare, protected and nocturnal.

Beach cusps: two explanations

Beach cusps are a row of evenly spaced sand points with scoops between them at the top of the swash, usually 1 to 50 m apart; wider swash gives wider spacing. One theory says the swash builds them itself, a self-organizing pattern. An older one says waves trapped along the shore set the spacing. The two predict similar spacings, and a field test favoring self-organization still found ambiguous signs of the trapped waves, so neither is settled. Nobody has recorded cusps on this beach.

See it yourself: After a few days of steady swell, walk the upper beach at low tide and pace off horn to horn.

Sand ripples: symmetric and lopsided

Under waves, water moves back and forth, so both sides of a ripple are worked in turn and the ripple is symmetric, with long straight crests that sometimes fork. Where water flows one way, in a creek or lagoon outflow, ripples have a gentle up-current side and a steep down-current side, and the steep side points the way the water went. On dry sand, wind ripple spacing grows in step with wind speed.

See it yourself: Compare ripples in a creek-mouth channel with those in the open swash zone. On breezy afternoons, look above the high-tide line.

Mud cracks: right angles first, hexagons later

When mud dries for the first time, each new crack tends to meet an older one at a right angle, making rectangles. If the same mud is wetted and dried again and again, the cracks reopen in a different order and the junctions drift toward three cracks meeting at 120°, closer to hexagons. In the lab this took about four wet-dry cycles.

See it yourself: Look at dried mud in road ruts or a dry creek bed by day, well back from any water. Count junctions: mostly T means a fresh crack set, mostly Y means repeated wetting. Near the lagoon, crocodile rules apply.

Why swell comes in sets

Swell is a mix of waves with slightly different periods. Where their crests line up, waves are bigger; where they cancel, there's a lull. Swell from far away has a narrow range of periods, so the grouping is strong. In deep water a group travels at half the speed of its crests, so waves appear at the back of a set, move through it and fade at the front. Grouped waves also make the water level at the shore rise and fall slowly over minutes, called surf beat. There is no fixed number of waves in a set; the "seventh wave" is folklore.

See it yourself: With a watch, count waves per set and the seconds between sets. Then mark the farthest swash with a stick for 10 minutes and watch it creep up and back.

Wave period sets wavelength

In deep water a wave's speed and length depend only on its period: speed is about 1.56 × period (m/s) and wavelength about 1.56 × period² (m). A 10-second swell has crests about 156 m apart; a 14-second swell about 306 m; a 20-second swell about 624 m. Longer waves travel faster, which is why the long-period part of a distant swell arrives first.

See it yourself: When the forecast shows long-period swell, time the seconds between crests passing a fixed rock and multiply the square by 1.56 to get the wavelength in deep water offshore.

Refraction: why the point peels

Waves travel slower in shallower water, so the part of a crest over shallow ground slows while the rest swings around it, and crests turn to line up with the depth contours. Wave energy converges on points and spreads in bays. A wave is surfable when it breaks progressively along its length; the peel angle is the angle between the trail of whitewater and the unbroken crest. If the bottom contours ran parallel to the crest, the whole wave would break at once, a closeout.

See it yourself: From high ground near the point, watch crests change direction as they wrap in. From the beach, follow one wave and note where the whitewater pauses and runs on.

Spilling or barreling

Whether a wave spills, plunges into a barrel or surges depends on the ratio of the seabed's slope to the wave's steepness, a number called the Iribarren (surf similarity) parameter. Gentle slopes and steep waves spill; steeper bottoms or longer, flatter swell plunge.

See it yourself: Watch from the side: a plunging wave throws its lip forward and leaves a tube of air.

Rip currents are less regular than theory

Rip currents form most often at low spots or gaps in sandbars and near structures. Theories predict regular spacing, but four years of daily images on one Australian beach found the spacing varied a lot and was not explained by simple models. This site holds no rip-current records for this beach.

See it yourself: Signs to look for from shore: a gap of darker, calmer-looking water between breaking waves, or foam moving out to sea.

Foam lines on the water

When wind blows over water, the surface layer can organize into long rolls turning in opposite directions, called Langmuir circulation. Where neighboring rolls meet and sink, foam and floating debris gather in lines running roughly with the wind, from a meter or two to hundreds of meters apart.

See it yourself: Once the sea breeze is up, look offshore from high ground for faint foam streaks pointing into the wind.

Foam: walls that meet at 120°

In foam that has drained, each bubble wall is a smooth film. Three walls always meet along an edge at equal 120° angles, and four edges meet at a point at about 109.5°. These are Plateau's laws, seen in the 1800s and proved by Jean Taylor in 1976. Fresh, wet sea foam has round bubbles; the polygons appear as it drains.

See it yourself: Look closely at sea foam stranded on the sand for a few minutes as round bubbles turn into many-sided cells.

Splash crowns

A drop hitting a thin layer of water throws up a crown-shaped sheet whose rim breaks into evenly spaced points, each shedding a droplet, through a Rayleigh–Plateau instability. The studies used lab drops on thin films; rain on deep water mostly makes a crater and a jet instead. Most wet-season rain here falls in the evening and at night.

See it yourself: On a covered porch at night, light a puddle from the side and use a phone's slow-motion video.

Lightning branches

A simple random model of electrical breakdown grows branching, fractal-like patterns, and real lightning looks fractal too. But there is no single fractal dimension of lightning: an earlier photo study gave about 1.3, and 3D mapping of one storm gave about 1.7.

See it yourself: Photograph distant storms at night from indoors; a long exposure shows the branching.

Cloud cells and storm spirals

Over parts of the open ocean, low cloud organizes into cells about 10 to 50 km across: cloudy centers with clear edges, or clear centers ringed by cloud. They resemble heated-fluid convection cells in a lab, though not exactly. Around a hurricane, rain organizes into a main band and smaller moving bands spiraling in toward the center.

See it yourself: Open a free daily satellite viewer and look at low cloud over the Pacific, or at a storm's radar loop, from indoors.

Lagoon channels branch, but not like rivers

Tidal channels branch like trees, which invites comparison with river networks and fractals. Studies of tidal lagoons and marshes in Venice, San Francisco Bay and Massachusetts found tidal networks don't follow rivers' clean scaling: the pattern breaks between large and small channels and differs from place to place.

See it yourself: Look at the lagoon on a satellite map. In person, only from a safe distance in daylight.

The wind clock

Every night the land breeze blows off the hills. Every morning, a little after ten, the sea breeze switches it off and the beach goes onshore until dusk, regular enough to set a clock by.

See it yourself: Note the time the palm fronds turn onshore each morning.

The tide clock

At the nearest tide gauge, in Zihuatanejo, the twice-daily tide is mostly driven by the sun, so low tides keep clock time, at about 1–4 in the morning and 1–4 in the afternoon in every month, instead of drifting about 50 minutes later each day as on many coasts. This comes from the site's model of that gauge, 20–25 km away.

See it yourself: Check a week of the forecast tide curve: the low-tide times barely move.