How to invert / change direction of the edges of an object using geometry nodes

Question

How can I invert / change the direction of the edges of an object so the outer pointing edges are pointing in and the inner pointing edges are pointing out.

Example below: The red arrows are pointing in the direction the altered edges should be pointing towards.

I tried multiplying the normal's by -1 but that didn't work.

Answers to @christopher-bennett qestions

1. The Koch fractal was created using Wannes Malfait free L-systems fractal add on. https://github.com/WannesMalfait/Blender-Add-ons/blob/master/L-System.py

Video of it in action

2. It's a mesh

Answers to @markus-von-broady Thanks to Markus I figured a way to show / animate (a smaller section) the process although not in Geometry nodes. (Instead of trying to do everything all at once separate each process out.)

How the invert would work.

1st part Inner going to outer

2nd Outer going to inner

Please note that this was just an example fractal I was looking for a general way to do this not just for one specific fractal since I would like to do the operation on other fractals.

Settings I used:

Attached blend file below:

Answer 1

To answer the specific example of the Koch Snowflake, you can build this fractal by designing a transformation which divides each edge into 4 segments, resizes first and last segment from ¼ to ⅓, and moves the center point along the normal so segments created by it have equal length to the former two.

Now initialize the used i attribute holding the number of the iteration (you could do without it by basing offsets on edge lengths, but why complicate things), and duplicate the node group a few times:

Now setting the scale of the 'extrusion' to negative will allow you to flip the side of this transformation:

You can also control which or from which iteration to flip:

Answer 2

Cunningham's Law…

You probably either want the distance to be calculated to a local origin (1) instead of the current average position (2), or you want more then just 1 vert/edge to flip (the entire half-star).

Answer 3

Another way to do this that will work on some fractals is to use a fractal that uses the same local origin for the points that will move.

Split the points up into outer going vertices and inner going vertices and "manually" (odd / even on this one) choose the points you want to adjust.

As stated by Markus there really is no general way to do this.