Create fractals with patterns driven by 3D sketches
A simple example of applying 3D sketch-driven patterns: creating the Sierpinsky pentagonal fractal from a generator dodecahedron.
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Step 1: Draw the generating dodecahedron
An alternative is to create it as an assembly of pentagonal plane figures:
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Step 2: Create a 3D sketch
Create a 3D point sketch using a dodecahedron scaled with respect to the generating dodecahedron:
Taking the generating dodecahedron and scaling it with a factor = 3.61803399
For the only time we will have to assemble this first scaled dodecahedron in order to find the insertion points of the generating dedecahedrons inside it:
Thus, we will have a part with a 3D sketch made up of points that we will use to drive a pattern of dodecahedrons instead of inserting and relating them manually:
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Step 3: Make successive patterns scaled with respect to the previous one
This same part, scaled again, will allow us to create a new scaled pattern based on the previous assembly.
- 20 generatric dodecahedrons inside a scaled dodecahedral 3D sketch f = 3.61803399
- 20 x 20 = 400 generatric dodecahedrons within a 3D sketch of a scaled dodecahedral shape f = 3.61803399 x 3.61803399 = 13,09016995279532
- 400 x 20 = 8000 generatric dodecahedrons within a 3D sketch of a scaled dodecahedral shape f = 3.61803399 x 3.61803399 x 3.61803399 = 47.36067982409016
