This effect creates fractals. The most classic fractal is perhaps the Von Koch snowflake. An alternative to using this LPE is to use the L-System extension.
Applying this effect to a path creates two additional control paths: a Reference segment and a Generating path. The structure of the fractal is completely determined by these control paths. The first generation is created by placing copies of the skeleton path so that the Reference segment of each copy lies on top of one of the sub-path segments of the Generating path. Each additional generation is created in the same way, using the Generating path of each copy of the previous generation.
When applying the VonKoch LPE to a path, the Reference segment is created so that it divides the bounding box vertically in half. The Generating path is initially composed of two single-segment sub-paths, each covering one-third of the lower edge of the bounding box. The Reference segment and the Generating path can be edited just like normal paths by clicking on the icon in the Reference segment or Generating path lines of the LPE dialog.
If each sub-path of the Generating path consists of a single segment, then each copy of the skeleton path is simply scaled and/or rotated. With multiple segments, one can skew each copy. The first path segment controls scaling in the orthogonal direction to the Reference segment and it controls skewing. The second path segment is matched to the Reference segment. The use of the first segment can be disabled by checking the Use uniform transforms only box.
Like all LPEs, this one can also be applied to groups.
Here is a short tutorial to create one side of a Von Koch snowflake:
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