Plutarch knew this wonderful Paxos beach, and over the centuries invaders from Venice to Britain have claimed it. Today, Monodendri is ruled by holidaymakers. But for how long?

Back away, hardbodies and musclemen: the seashore's a geek paradise. Here are the non-linear equations of catastrophe theory, in the breaking waves; here's turbulent flow, one of the last frontiers of mathematical modelling. Here are countless Fibonacci series, the one where each new number is the sum of the two preceding ones: 1,1,2,3,5,8,13, expressing itself in shells, pine cones and flower petals.

Most of all, the beach is the home of fractals: patterns which repeat themselves at smaller and smaller (or larger and larger) scales. The coastline on a map; a bay or a cove on a larger-scale map; a fraction of the shoreline seen close-up. All show the same pattern, at different sizes.

But the beach is a four-dimensional fractal; it repeats itself over different timescales, too. Here's Monodendri Beach on the north-east coast of Paxos, a tiny island in the Ionian Sea, just south of Corfu. Two thousand years ago, a sailor, Thamus, was sailing past Monodendri (he'd have avoided the west coast, a treacherous lee shore) when, says Plutarch, a mysterious voice hailed him across the water, saying "When you reach Palodes, be sure to tell them the great god Pan is dead".

All the olive trees in all the olive groves, all the rocks on this rocky island, cried out in a terrible lamentation. Then nothing.

The beach, unnamed, sits quietly, simply being itself. Over the centuries a handful of people come and go. Suddenly (suddenly, in geological time) peasants arrive, then priests. Venetians follow, then an English governor, then the war and the Germans, and now it's high noon, tourists and second-homers from the British Isles and Italy and Russia; in due course the global night will fall; Monodendri will return to the islanders, the islanders will return to a grubbed-up peasant life, then they too will go and once more Monodendri Beach will have no name. Nor will it be a beach. A beach needs humanity to make it so. Without us, it will revert to its nameless self: a seashore.

Over the past 20 years, year on year, this beach has been changing. At first you could reach it most easily by boat, or by scrabbling down a precipitous path through the olive groves to the sea. If you were lazy or infirm you could go by donkey, if you had a donkey. There were no cars. On the beach were pebbles and driftwood; in the sea were octopus; al fresco beach dining required a spear-gun and a box of matches.

It wasn't Monodendri then, not officially. Paxos is not a place much given to fancy names; other than its main town, Gaios, its three main habitations' names, they tell me, mean "scrub", "clearing" and "shops". Monodendri means "one tree". Presently, it got a sign that read "paralia", painted on plywood, pointed vaguely downhill: "beach". A few years ago, a better-painted sign appeared, then a better-painted and bigger sign pointing to Taverna Bastas – the enterprising Bastas family had set up shop there and the visitor would be greeted with a row of octopus, hanging on lines like submarine revenants, draining in the sun.

Now, with hard work and EU grants, there is mains water, if the island reservoirs haven't evaporated and the electricity supply hasn't been shut off or its cable broken, somewhere under the sea between Paxos and the mainland. Last year, they built a swimming pool, of no interest to the well-to-do in their blue-pooled villas (on this island where water is a perpetual source of worry) but a wonderful lure to families on a budget and to local Paxiot families, too. The taverna is friendly, the Bastas family tireless. One-Tree Beach – reached now by a bitumen road, with a proper white-on-blue sans-serif European road sign – prospers, and has been declared one of the world's best beach-front tavernas. It rises. But, as on the millennial scale, it will fall again as the money runs out and the oil runs out and the planes are grounded and the seas rise.

In the winter, from November to the end of February, it rains, though 'rains' doesn't really describe what it does on Paxos. The tourists and the villa folk pack, close up their houses and catch the precarious hydrofoils – former Eastern Bloc riverboats, the maritime equivalent of steel drums, which occasionally break down altogether and drift amiably towards Venice – back to Corfu, the unspeakable Ioannis Kapodistrias airport, and home.

The islanders move inland. Life moves away from the lashing sea and into the endless rain, the colour and temperature of English rain but with a relentless enthusiasm more associated with Phnom Penh or Darwin in the Wet. Monodendri is a deserted irrelevance. Nobody ventures out. The rains are a time of endless DVDs and satellite sports for the more sober; for those in whom the blood is still hot, it is a time of assignations in empty villas. April always sees tricky reckonings; sometimes one or other party will disappear in the night, to resurface on Poros or Skopelos or in a second cousin's first husband's shoe-shop in Athens.

Then, in May, the tourists. The wire-mesh barriers are removed, the taverna scrubbed and prepared, the pool cleaned, the stock ordered in. Shyly at first, they appear; in May it's mostly regulars who spend half the year on the island, and English school teachers on walking-tours to see the spectacular wildflowers.

Elderly couples come on off-peak holidays – she gingerly tries the octopus, while appeasing him, scowling at his kebab, peering at his chips as though they might impugn his mother. Then come the British in June and even more British and French in July, and August is for the Italians in preposterous SUVs and the richer mainland Greeks: no-longer-young plutocrats with enormous gold watches and tiny third wives in proportionately tiny bikinis, motoring in from the sea in tremendous roaring 2,000HP speedboats, exulting in their worldly success and their persisting virility, subject to smiles of amusement from the spectators in the cheap seats, warming their souls with a cool Mythos and a plate of tzatziki.

In September it fades gently, the sea still warm, the nights mercifully cool. Then, in October, on an unfixed date silently agreed upon all over the island by some sort of telepathy, the shutters suddenly go up...

...and so, too, the weeks and the days. The die-hards in the morning, jogging down (and up again) the steep track for their morning swim; then the families, brought up from Scrub or Clearing. Come lunchtime, first the foreigners, who've spent the morning heating up in their villas, then the Greeks, who eat later. At the weekends and on Mondays – when the visitors change over and Corfu airport becomes a giant intolerable sweatbox – the Paxiots take their break: gia-gias competitively displaying their grandchildren, old chaps in singlets, young men fresh from national service, strutting in their Hawaiian trunks, old men, life-support systems for bellies and Type 2 diabetes, in ill-judged Speedos. And in the evening, a little further on, past the point and up a little into the groves, Ben's Bar fills up with the young, flirting and smoking and the pulse of music drifting across the warm night.

And then darkness. The young drift away. The tavernas are cleaned down. The holidaymakers head home. The rain comes. The oil runs out. The millenia turn. The fractal beach continues on its path, warming our northern souls, being nibbled away by the remorseless sea. All human life is here, if only for a while.