Archipelagos: Cruising the Infinite

Posted by DimensionT at HomeBrewHeaven

Inchworm, Inchworm, 

Measuring the marigolds;
Seems to me you'd stop and see 

How beautiful they are.

Children's Song

Archipelagos: Cruising the Infinite

That object pictured above and being overrun by vines is called a Menger/Sierpinski Sponge, a construct with literally infinite surface area. Or none. I won't go deeper into it (No thanks necessary. Really.), other than to say that it's fractal, which slides us right into the Coastline Paradox.

How long is a given stretch of coastline? The paradox is that there is no single answer... like the sponge, it has literally infinite length. But as a practical matter, it depends on how you measure it. 

If we measure along it using a ruler that is one nautical mile long, we'll arrive at a figure, but miss hundreds of little coves. All the best ones, I might add.

Well, okay. How about a hundred meter ruler? Now we're talking! The coast is suddenly a LOT longer. We're starting to sneak into some of those cozy harbors we missed on the first round. Each new nook and cranny adds length to our total. But still... there are several interesting little spots that a football field is just too large to squeeze into.

A boat length? Now we can shore tie and enjoy the merest notch. The coast stretches on and on. Or better yet, a double butt-width (mine and my Sweetie's, side by side)! We can sail up, row ashore and hike to a zillion beautiful places to set ourselves down and enjoy along a coastline which is, from our point of view, endless. Our brief lives will never be enough to absorb a fraction of that abundance, rolling on toward infinity.

Archipelagos are wondrously intricate places. Complex, even as coastlines go, they convolute in concealing crenelations! Channels twist and turn among them. Any stretch of water may find itself, round the next corner, ending in a cul de sac, branching into a labyrinth, opening onto wide horizons. And the smaller your own scale, the more is available to you.

Archipelagos clump themselves in... archipelettes? Small clusters of islands every bit as complex, on smaller scale, as the whole. Mountain ranges and reefs are all a matter of scale; the sea - itself a pan-fractal being - floods between them both the same. The smaller the unit of measure, the more intricate and intimate it becomes. The tide running in to cover the flats races and eddies; look closely and one sees every feature of the world about, writ small and smaller.

One beautiful summer day, we anchored LUNA and rowed ahead to scout some tricky narrows in Rocky Pass. They're big tidal races, shallow, rocky and have some dangerous 90deg turns. "Devil's Elbow" is such an evocative name, don't you think? 

We wouldn't pass through till next day, so on our return just let the dory drift on the fair current among the islands. We meandered far from the straight line home, doubling back in lazy eddies, skirting reefs and bars and all manner of granitic rubble. No matter. When ready, we'd row from wherever we ended up. Though our path was mazed, distant mountain peaks would guide us home.

We breathed in fragrance from duff of spruce and hemlock and fragrant wildflowers. Warmed and lulled, we dozed; merely cocked an eye at whatever soft bump against island or outcrop. But each time, the water carried us gently on. Finally, a cool shadow intruded on my dreams. I woke to find ourselves at arms length from LUNA.

Inching along in our little home, worming amongst the twists and turns, exchanging one scale for another with each turn of the head, we can't help but notice how beautiful are the marigolds.

Some of Rocky Pass
Running between two larger islands, it contains hundreds of islets, thousands of rock outcroppings, millions of stones, billions of pebbles, trillions of...