Gosper Curve

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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