The Hammock Papers: Fractals.

25 June 2014

Fractals.

Look at the honeycomb pattern in a beehive, say, and the hexagonal structure is only visible if you're not too close or too far away. But look at some kinds of plants and you'll see their fronds are made up of ever-smaller versions of the overall leaf. This is known as scale invariance, and is a feature of fractals. Richardson noticed that coastlines have a similar property, their jagged outlines appearing just as jagged as one zooms in to ever-smaller scales.

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WOLFGANG AMADEUS MOZART

"When I am, as it were, completely myself, entirely alone and of good cheer – say travelling in a carriage or walking after a good meal, or during the night when I cannot sleep – it is on such occasions that my ideas flow best and most abundantly. Whence, and how, they come I know not ; nor can I force them. Those ideas that please me I retain in memory and am accustomed, as I have been told, to hum them to myself. If I continue in this way, it soon occurs to me how I may turn this dainty morsel to account, so as to make a good dish of it. That is to say, agreeable to the rules of counterpoint, to the peculiarities of various instruments etc. All this fires my soul, and, provided I am not disturbed, my subject enlarges itself, becomes methodised, and defined, and the whole, though it be long, stands almost complete and finished in my mind, so that I can survey it like a fine picture or a beautiful statue at a glance. Nor do I hear in my imagination the parts successively, but I hear them, as it were, all at once. What a delight this is, I cannot tell."

MARCUS AURELIUS

"Is your cucumber bitter? Throw it away. Are there briars in your path? Turn aside. That is enough. Do not go on and say, 'Why were things of this sort ever brought into this world?' neither intolerable nor everlasting - if thou bearest in mind that it has its limits, and if thou addest nothing to it in imagination. Pain is either an evil to the body (then let the body say what it thinks of it!)-or to the soul. But it is in the power of the soul to maintain its own serenity and tranquility."

VINCENT van GOGH

"What am I in the eyes of most people? A nonentity or an oddity or a disagreeable person — someone who has and will have no position in society, in short a little lower than the lowest. Very well — assuming that everything is indeed like that, then through my work I’d like to show what there is in the heart of such an oddity, such a nobody. This is my ambition, which is based less on resentment than on love in spite of everything, based more on a feeling of serenity than on passion. Even though I’m often in a mess, inside me there’s still a calm, pure harmony and music. In the poorest little house, in the filthiest corner, I see paintings or drawings. And my mind turns in that direction as if with an irresistible urge. As time passes, other things are increasingly excluded, and the more they are the faster my eyes see the picturesque. Art demands persistent work, work in spite of everything, and unceasing observation."

DAN CAMPBELL