Poem fractal
0.023 apart. A smaller distance means the lines are built more alike.
This number is read from the build of the lines. The bright edge is that number, carried outward until the pattern repeats.
−0.1105 − 0.6499i
Drawing the boundary…
by John Keats
−0.1186 − 0.6711i
Drawing the boundary…
Each poem scrolls on its own, so the two texts stay beside each other.
The wind is rising on the sea,
White flashes dance along the deep,
That moans as if uneasily
It turned in an unquiet sleep.
Ridge after rocky ridge upheaves
A toppling crest that falls in spray
Where the tormented beach receives
The buffets of the sea’s wild play.
On the horizon’s nearing line,
Where the sky rests, a visible wall.
Grey in the offing, I divine
The sails that fly before the squall.
by John Keats
O what can ail thee, knight-at-arms,
Alone and palely loitering?
The sedge has withered from the lake,
And no birds sing.
O what can ail thee, knight-at-arms,
So haggard and so woe-begone?
The squirrel’s granary is full,
And the harvest’s done.
I see a lily on thy brow,
With anguish moist and fever-dew,
And on thy cheeks a fading rose
Fast withereth too.
I met a lady in the meads,
Full beautiful—a faery’s child,
Her hair was long, her foot was light,
And her eyes were wild.
I made a garland for her head,
And bracelets too, and fragrant zone;
She looked at me as she did love,
And made sweet moan
I set her on my pacing steed,
And nothing else saw all day long,
For sidelong would she bend, and sing
A faery’s song.
She found me roots of relish sweet,
And honey wild, and manna-dew,
And sure in language strange she said—
‘I love thee true’.
She took me to her Elfin grot,
And there she wept and sighed full sore,
And there I shut her wild wild eyes
With kisses four.
And there she lullèd me asleep,
And there I dreamed—Ah! woe betide!—
The latest dream I ever dreamt
On the cold hill side.
I saw pale kings and princes too,
Pale warriors, death-pale were they all;
They cried—‘La Belle Dame sans Merci
Thee hath in thrall!’
I saw their starved lips in the gloam,
With horrid warning gapèd wide,
And I awoke and found me here,
On the cold hill’s side.
And this is why I sojourn here,
Alone and palely loitering,
Though the sedge is withered from the lake,
And no birds sing.
A fractal is a shape that keeps its pattern when you look closer. Coastlines, trees, shells, and weather do this. The large form and the small form are the same kind of thing. A poem can be drawn that way. The shape of the whole comes from the shape of the lines.
Primunia is the name for the source of that order: the pattern under the pattern, already there in a tree, a shell, and a verse.
The number under the picture is the poem constant. It is read from the build of the lines: their length, how uneven they are, the size of the stanzas, the share of vowels, and the way the lines end. A new word moves the number when it changes that build. The same poem always gives the same number.
Drawn on its own, that number sits in a quiet part of the plane, and most poems would look like the same soft disk. So the number is carried outward along its own direction until it meets the edge of the Mandelbrot set, where the shape turns sharp. The picture is the Julia set of that meeting place.
Each point on the canvas is folded again and again by one small rule. Points that stay near the rule form the dark interior. Points that rush away become the coloured bands. The hue comes from the poem constant, and the brightest bands turn toward gold. Change the length of a line, the stanza, or the vowel share, and both the number and the picture move.
Branching draws the poem as a tree. Each turn follows a line, and every smaller branch repeats that pattern. A longer line reaches farther. The letters at the start of a line bend the next turn. A higher share of vowels opens the branches wider.
The trunk takes its colour from the poem constant and warms toward gold at the tips. When the poem has more than one stanza, gold forks leave the trunk. Each fork is a stanza beyond the first, up to three. The tree divides where the poem divides. One stanza remains a single trunk.
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