Algorithms and Data Structures

N.Wirth. Algorithms and Data Structures. Oberon version 106
Fig. 3.5. Sierpinski curves S 1 and S 2 .
The base pattern of the Sierpinski curves is
S: A B C D
and the recursion patterns are (horizontal and vertical arrows denote lines of double length.)
A: A B → D A
B: B C ↓ A B
C: C D ← B C
D: D A ↑ C D
If we use the same primitives for drawing as in the Hilbert curve example, the above recursion scheme is
transformed without difficulties into a (directly and indirectly) recursive algorithm.
PROCEDURE A (k: INTEGER);
BEGIN
IF k > 0 THEN
A(k-1); Draw.line(7, h); B(k-1); Draw.line(0, 2*h);
D(k-1); Draw.line(1, h); A(k-1)
END
END A
This procedure is derived from the first line of the recursion scheme. Procedures corresponding to the
patterns B, C and D are derived analogously. The main program is composed according to the base
pattern. Its task is to set the initial values for the drawing coordinates and to determine the unit line length h
according to the size of the plane. The result of executing this program with n = 4 is shown in Fig. 3.6.
VAR h: INTEGER; (* ADenS33_Sierpinski *)
PROCEDURE A (k: INTEGER);
BEGIN
IF k > 0 THEN
A(k-1); Draw.line(7, h); B(k-1); Draw.line(0, 2*h);
D(k-1); Draw.line(1, h); A(k-1)
END
END A;