This effect creates fractals. The most classic fractal is perhaps the
Von Koch snowflake. An alternative to using this LPE is to use
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.
Left: A skeleton path.
Center: After applying the VonKoch with default parameters.
Right: Showing the default Reference segment (top line) and
Generating path (bottom two lines).
When applying the VonKochLPE 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
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.
Left: A diamond path with the VonKoch LPE applied.
The default control paths are shown.
Center: After moving the Generating paths.
Right: After increasing the number of generations to six and changing the
Fill and Stroke.
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.
Left: A square path with the VonKoch LPE applied.
The default control paths are shown.
Center: After editing the Generating path to add
a second path segment to each sub-path.
Right: After increasing the number of generations to two.
Like all LPEs, this one can also be applied to groups.
Left: A fourth generation Sierpinski triangle (triangle with three Generating paths).
Right: The same VonKoch LPE applied to a group consisting of a triangle and circle.
Here is a short tutorial to create one side of a Von Koch snowflake:
Create a regular six-pointed star using the Star Tool (set Spoke ratio to 0.577).
Convert star to a path (Path →
Object to Path
(Shift+Ctrl+C)); remove nodes as shown in figure below
(use and from the Node Tool-Tool Controls).
Left: A regular six pointed star.
Right: The skeleton path after deleting nodes from the star.
Make a duplicate of the path as we will need a copy later; move it aside.
Apply the VonKoch effect to the original path, this will create default control paths.
We need to edit both control paths, it is perhaps slightly easier
to start with the Generating path. This
control path, by default, consists of two separate path
segments. We need four segments exactly like in
the skeleton path. Select the duplicate of
the skeleton path and use
on each of the middle three nodes. When you are finished, the
Status Bar should report the path consists of eight nodes.
Copy the duplicated path to the clipboard; select the original path
and in the Path Effect Editor dialog click on the in the
Generating path line. This will replace the default
path. You will probably see the first-generation paths jump to the upper-right
corner. Don't panic! We'll need to drag the Generating path
to where it belongs.
Click on the icon in the Generating path
line of the LPE dialog. You should see the Generating path
as a green path. Select all the nodes and drag them to overlap the
Left: After copying the skeleton path and
applying the VonKoch LPE. Both
the Reference segment
and Generating path are shown
(the skeleton path Stroke has been set
to gray so it is easier to see
the control paths).
Right: The duplicate of the skeleton path
has been separated into four sub-paths. It was then pasted
into the LPE to replace the Generating
path. The resulting Generating
path has been translated as shown.
Next we need to edit the Reference
segment. Click on the icon in
the Reference segment line of the LPE
dialog. Select both nodes and move them down to them to overlap
the base of the skeleton path.
Finally, you can increase the number of generations. If you
select four or more generations, you will have to increase
the Max complexity value. You can also
uncheck the Draw all generations box.
Left: After the Reference segment has been moved.
Right: The final result with the number of generations set to 3 and the
Draw all generations unchecked.