Definition:Koch Snowflake

Definition

The Koch snowflake is the fractal generated by:

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This is the $3$rd iteration of the Koch snowflake:

Also known as

The Koch snowflake is also known as:

the Koch curve

the snowflake curve.

Also see

• Fractal Dimension of Koch Snowflake

• Results about the Koch snowflake can be found here.

Source of Name

This entry was named for Niels Fabian Helge von Koch.

Historical Note

The Koch snowflake was introduced by Helge von Koch in $1904$.

Hence he demonstrated that a curve of infinite length can enclose a finite area.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Koch curve
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): fractal
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Koch curve
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): fractal
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Koch curve