The fractal I chose to print is the Barnsley Fern. I love how simple this object is from afar and how intricate it gets when you really look at it.
I believe this is a fractal because it can be constructed by a pattern of identical shapes continuously placed on top of and next to each other.
As stated in the wikipedia page for this fractal, it was created by British mathematician Michael Barnsley in 1988. It was included in his book Fractals Everywhere, which described different fractals that can simultaneously be seen in nature and artificially produced.
I love how the Barnsley Fern is relatable to human life – it resembles a plant that most of us have seen first hand, but it also has a complex mathematical background.
The photo below shows the Barnsley Fern in four succesive stages of its development.
As you can see with the bright color used, the object gets thicker with each stage. This is because, like any fractal, tiny patterns are replicating over themselves.
This video gives you an opportunity to look deeper than the surface level of the Barnsley Fern and see how it is constructed.
This video is also helpful because it provides the math behind the fractal construction.
I am not sure that this fractal will print because I do not know how intricate of a design the printer will be able to produce. However, this fractal is known to be very versatile and can be printed at many sizes.
UPDATE: This fractal was not able to be printed because of its intricacy and lack of models available on the internet. However, I did print a few other less complicated fractals: two variations of the sixfold fractal and a Sierpinski triangle.
These models took anywhere from 20 to 40 minutes to print and are quite small. The smallest is the orange sixfold fractal, measuring about 3 inches in diameter. Because of its intricacy it took the longest to print out of all three (about 40 minutes).
Although I was not able to print my initial chosen model, I was still able to get a deeper look into the process of 3D printing fractals, and I was able to watch each layer of the fractals come together.