What is the Koch curve?
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The Koch curve is a mathematical fractal and a classic example of a space-filling curve. It is constructed by starting with an equilateral triangle and recursively altering each line segment.
Construction Steps:
Start with an equilateral triangle.
Divide each side into three equal segments.
Create an outward equilateral triangle on the middle segment, effectively replacing it with two new segments.
Repeat this process for each straight segment of the shape.
Characteristics:
The Koch curve has an infinitely intricate boundary, meaning it becomes increasingly detailed with each iteration.
It has a finite area but an infinite perimeter, illustrating the concept of fractals where simple rules lead to complex structures.