Flocken ohne Ende

Ich bin jetzt alle Beispiele durchgegangen, die auf der deutschen Wikipedia-Seite zu Fraktalen aufgeführt wurden, welche sich geometrisch konstruieren lassen. Hiermit ist quasi bewiesen, dass die dort angegebenen Regeln (auch „L-Systeme“ genannt) zur Konstruktion alle korrekt sind, wobei nicht alle Fälle selbsterklärend sind. Speziell die Hilbert und die Peano Kurve wichen plötlich von der Notation ab: zuerst gab es die Strecken-Variablen L und R und hier auf einmal X, Y UND F. Desweiteren ging man vorher von gleichen Seitenlängen für R/L aus, wobei X/Y plötzlich gar keine Länge mehr hatte und dafür nur noch F abgetragen wurde.

Aber schliesslich habe ich alle Systeme anwenden können. Hier sind die Ergebnisse:

Hilbert Kurve:

Hilbert Kurve

Streckenlänge: 4 Pixel
Iterationstiefe: 6
Winkel: 90°

Gosper Kurve:

Gosper Kurve

Streckenlänge: 5 Pixel
Iterationstiefe: 4
Winkel: 60°

Peano Kurve:

Peano Kurve

Streckenlänge: 3 Pixel
Iterationstiefe: 4
Winkel: 90°

Koch Kurve:

Koch Kurve

Streckenlänge: 3 Pixel
Iterationstiefe: 4
Winkel: 60°

Penta Plexity:

Penta Plexity

Streckenlänge: 10 Pixel
Iterationstiefe: 3
Winkel: 36°

Pfeilspitze:

Pfeilspitze

Streckenlänge: 5 Pixel
Iterationstiefe: 6
Winkel: 60°

Sierpinskidreieck:

Sierpinskidreieck

Streckenlänge: 5 Pixel
Iterationstiefe: 5
Winkel: 60°

Sierpinskiteppich:

Sierpinskiteppich

Streckenlänge: 3 Pixel
Iterationstiefe: 4
Winkel: 90°

Lévy C Kurve:

Lévy C Kurve

Streckenlänge: 3 Pixel
Iterationstiefe: 12
Winkel: 45°

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