This project is a recursive raindrop fractal designed in OpenSCAD. It was inspired by the ideas of Iterated Function Systems (IFS) that we studied in class. In my design, a simple 2D raindrop shape serves as the base. The fractal is formed by repeatedly shrinking and translating copies of this base shape, similar to how we studied the hexagon fractal and the Barnsley fern. I chose a raindrop because it is a natural, smooth shape that looks visually striking when layered with recursion. The mathematics behind this project uses contraction mappings, which always guarantee convergence to a fixed fractal attractor (Banach Fixed-Point Theorem). Each new raindrop is created by applying a scaling, translation, and small rotation: (x', y′)=(s⋅x+t_x​, s⋅y+t_y​).
where s=1/2 ​ is the shrink factor, and (t_x ​,t_y ​ ) are translations that place the new drops relative to the parent. A small rotation is also applied using the standard matrix R(θ) = [cosθ, −sinθ; sinθ, cosθ].
These transformations are applied recursively so that after 𝑛 n steps, the size of the raindrop is s^n ⋅L, where L is the original length. Because 0<s<1, the shapes always shrink and converge toward the tip of the raindrop fractal.

From the class readings (Part 1 Introduction, Part 4a and 4b on IFS, and the Barnsley fern handout), learned that an Iterated Function System is a set of rules that transform a base shape repeatedly to create a self-similar fractal. The theory shows how fractals are created by contraction maps, and that every set of contractions converges to one unique fractal attractor. In my case, the attractor is the recursive raindrop pattern. The raindrop base was coded by using two circles and taking their hull, which makes a smooth teardrop curve. I then applied transformations such as scaling by a factor of 1/2 for each recursive step Translating the smaller drops upward or sideways to form the layered look Rotating slightly at each step to keep the drops curved into the shape. In addition to the class material, I also looked up simple geometry resources on how to make smooth teardrop shapes. Using curves and the hull operation in OpenSCAD is a common way to build natural forms like leaves or raindrops. This extra research helped me make the raindrop fractal look a bit more natural.

When printing, the base thickness was set to 5 mm to meet the class requirement, and the largest direction measured about 118 mm. The print took about 4 hours and 37 minutes and used 28 g of filament (9.32 m). I did not need a raft or supports since the shape prints cleanly on a flat base. Both the STL file and the OpenSCAD code are included in this Thingiverse entry. For best results, I recommend a 0.2 mm layer height, 20% infill, and at least 3 solid bottom layers to give stability to the base of the raindrop fractal. If I were to print this again, I would try lowering the print speed slightly and increasing the infill to 25% so the smaller raindrop details come out sharper and sturdier.