The Gosper curve, named after Bill Gosper, also known as the flowsnake (a spoonerism of snowflake), is a space-filling curve. It is a fractal object similar in its construction to the dragon curve and the Hilbert curve.
A fourth-stage Gosper curve | The line from the red to the green point shows a single step of the Gosper curve construction. |
A Logo program to draw the Gosper curve using turtle graphics (online version):
to rg :st :ln
make "st :st - 1
make "ln :ln / 2.6457
if :st > 0
if :st = 0
end
to gl :st :ln
make "st :st - 1
make "ln :ln / 2.6457
if :st > 0
if :st = 0
end
The program can be invoked, for example, with rg 4 300
, or alternatively gl 4 300
.
The constant 2.6457 in the program code is an approximation of √7.
Read more about Gosper Curve: Properties
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