Ricktu has got a great idea to design a single line with contiuous cross section 3D fractal. It prints well when sliced with cura, but is not perfect when sliced with slic3r.
I then designed my own under openscad. It's a quite simple very small code using a recursive module.
Please, watch the video to see it printed and you'll get the idea of this fractal spiral mode object ! https://youtu.be/ihfkdBEPOOo
As it is designed with Openscad it becomes a customizable object where you can parametrize the width of the smallest pyramid and the fractal order.
- size parameter is the radius of the smallest pyramid in the fractal
- order defines the number of recursive iterations
The one you see in the first picture has been printed with a 3mm radius and a fractal order of 5. It's already a big object of 135mm which printed during 9 hours and 30 minutes.
[size = 3 order = 5] will buid a pyramid = 2^5 x 1.414 x 3mm = 135 mm of side lenght
EDIT 171117 : fixed a bug, now slices perfectly at size = 2
You'll have to set your slicer to spiral vase mode. No top layer, one single bottom layer.
Layer thickness has to be set à 0.2 mm
what is spiral vase mode ?
the Spiral Vase setting of Slic3r will raise Z continuously avoiding a layer-change point which would cause a visible seam.
To allow this 3D fractal to be printed in spiral mode, it is needed that every layer is a continuous non crossing pattern. Which is the case here as every layer is a Sierpinski 2D fractal known as a Sierpinski curve. (see: https://en.wikipedia.org/wiki/Sierpi%C5%84ski_curve)
Sierpiński curves are a recursively defined sequence of continuous closed plane fractal curves discovered by Wacław Sierpiński, which is an example of a space-filling curve.
Finally, the printer will follow a single continuous line from its entry point (red arrow at the bottom layer) up to the pyramid summit (red arrow on top).
This makes a mesmerizing print !