Customizable Mandelbrot Set - Apfelmännchen
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This is my first OpenSCAD-based design. What's special about this variant of the Mandelbrot Set visualization is that…
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This is my first OpenSCAD-based design.
What's special about this variant of the Mandelbrot Set visualization is that it doesn't show a lot of the spikes of other designs due to the "Height Power Scale" non-linear scaling parameter and also a bit due to the high iteration parameter. As a result, it's also very printable (standing up gives best results).
When using the customizer, you will probably want to increase the resolution to something between 6 and 10. I used a low default value to make the preview appear quicker.
Because the math is calculated on the fly, you can use the customizer to zoom and pan around in the Mandelbrot Set space. Zoom in to find (and print) self-similar shapes!
Print Settings
Printer Brand:
Creality
Printer:
CR-10 Mini
Rafts:
No
Supports:
No
Resolution:
0.15mm
Infill:
15%
Notes:
For the shown print, I used a resolution parameter of around 8.
I printed this example standing upright (with brim) to achieve better resolution and a nicer surface finish. I also cut off about half of the base to save on filament.
If you print this flat on an FDM printer, expect a lot of coarse blobs (even if your printer is not prone to blobbing) due to customary extrusion widths of between 0.4 and 0.5mm.
How I Designed This
This was programmed from scratch in OpenSCAD.
While modules like using polyhedron for surface-mapping have already implemented a hundred times in this environment (and also available using a simple surface() call), I chose to be the one-hundred-first one to implement it, just to get experience with polyhedra generation in the beautiful weirdness that is the OpenSCAD language.
Where it actually pays of to implement it from scratch, is that all calculations to create the Mandelbrot shape are done on the fly. There is no static image that has been fed to a surface mapper.
And while calculating the Mandelbrot Set yourself isn't exactly rocket surgery, it offers the flexibility to actually pan and zoom around in this self-similar shape, find something beautiful, and print the result.
Category: Math Art