O beautiful for spacious skies, For amber waves of grain, For purple mountain majesties Above the fruited plain! America! America! God shed His grace on thee And crown thy good with brotherhood From sea to shining sea!
O beautiful for pilgrim feet, Whose stern, impassioned stress A thoroughfare for freedom beat Across the wilderness! America! America! God mend thine every flaw, Confirm thy soul in self-control, Thy liberty in law!
O beautiful for heroes proved In liberating strife, Who more than self their country loved, And mercy more than life! America! America! May God thy gold refine, Till all success be nobleness, And every gain divine!
O beautiful for patriot dream That sees beyond the years Thine alabaster cities gleam Undimmed by human tears! America! America! God shed His grace on thee And crown thy good with brotherhood From sea to shining sea!
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Track 1
How this picture is made
What a fractal is
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.
How the boundary is drawn
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.
What the branching signifies
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.