Mini 2 - “Lasered!”

A parametric snowflake ornament generator

Task 1

A parametric snowflake generator

For my project, I developed a parametric snowflake ornament generator. By inputting a set of parameters, the program is capable of generating a unique snowflake design, which includes a mounting hole. The foundational algorithm for creating the geometry derives from the Koch Snowflake, a concept first introduced by Helge von Koch in 1904 . This fractal pattern is generated by beginning with an equilateral triangle. The process involves removing the middle third of each side, then constructing an additional equilateral triangle at the point of removal, and repeating these steps. The image below illustrates the first four iterations of this method.

I wanted to create a program that could employ this pattern to create laser-cut Christmas tree ornaments. To do this, I would need to wrap the pattern around a polygon so that I could create the multiple arms of a snowflake. My program starts by drawing an N-sided polygon. The radius of the polygon is also a parameter. I then employ the Koch algorithm to convert the starting line into a fractal. The process of recursively replacing lines with deeper fractals is repeated for K steps. The final result is a fractal snowflake with multiple starting arms. To make the snowflake hangable on a tree, I also added code to automatically add a hole inside one of the arms of the snowflake. Depending on the number of sides (N) specified, the exact location of this hole is calculated and drawn. Finally, I wanted the ability to control the surface finish on the laser-cut piece. I added a Boolean parameter that adds a background to the snowflake. If the user wishes to create a frosted effect, they can enable the background and use that to etch with the laser cutter. Otherwise, they can disable the background and simply cut the snowflake out.

The code

I drew some inspiration from this processing example that employs the Koch pattern on a single line: All code was written by me.

Example designs

The five example designs below demonstrate the various parameter configurations. The designs with the blue background will be etched/ frosted when fabricated.

Task 2

I used 3mm acrylic for my assignment. Each snowflake is 5.5” x 5.5”

Clear snowflake

This snowflake is 260 mm across, 5-arms, with a recurison depth of 4 and a 8 mm hanging hole. No background was used, therefore no etching was done.

Frosted snowflake

This snowflake is 260 mm across, 6-arms, with a recurison depth of 2 and a 8 mm hanging hole. A background was used to etch and create the froted effect. This design is both etched and cut.