The Van Koch Line Fractal

The Van Koch line fractal is another simply fractal. It involves a line and breaking a piece of this line.

Here is a brief explanation of how this fractal works.

First you start with a simple line (fig.1).

Fig. 1

Then, break the line into 3 segments (segments AB, CD, DF, in fig. 1b).

Fig. 1b

Then bring the middle segment (segment CD) up . Join the right end point of the left segment (fig. 2, pt B) with the left end point of the middle segment (fig. 2, pt C) to make a segment BC. Then do the same with the right end point of the middle segment (fig. 2, pt D) with the left end point of the right segment (fig. 2, pt E) to make segment DE.

Fig. 2

Repeat the previous step for the each of the three segments and you will get as a result figure 3.

Fig. 3

Then repeat again...

Fig. 4

And again...

Fig. 5

This process is suppose to be done infinitely. What you get as a result is the Van Koch line fractal.

We have a created a program on Maple V Release 4 that does this. Please see Fractal Programs for more details.