Reflexive Ghost

George Mason University Math 401: Mathematics Through 3D Printing

This print was designed to replicate the fascinating optical illusion known as a Kokichi Sugihara Reflexivity-Fused Object. As Sugihara himself described it, "The objects themselves have meaningless shapes, but if they are placed on a horizontally oriented mirror, meaningful shapes appear." Using the power of Mathematica, I began creating my version of this intriguing object.

To begin, I employed Mathematica to plot two separate equations, namely g1 and f1. The f1 equation is positioned on top, while g1 represents the reflected image in the mirror. In this particular case, the equations took the form of:

f1 = 2.7 Sin[t] - 1.2
g1 = 0.5 Cos[8 t] + Sin[t]

These equations were then skillfully woven into the following command: "ParametricPlot[{{Cos[t], f1}, {Cos[t], g1}}, {t, 0.418, 2.733}]" within Mathematica.

With these mathematical foundations in place, I proceeded by setting alpha to 1/Sqrt[2] and the heig