[Mathematical Art] Light Tower

thingiverse

My website: http://jlu227.wix.com/kay-lu Hi visitors! Since I am developing my website currently, I encourage you to visit my website and leave comments there! <3 :) I was inspired by an applied complex variables class! :D Specifically, I was inspired by w = sin(z), z=x+iy, x,y are real numbers. This function maps horizontal lines in the z-plane to ellipses in the w-plane. My initial idea is to visualize this mapping (although impossible since it is 4-dimensional) by setting the z-plane and w-plane just parallel to each other, and then drawing horizontal lines on the z-plane and corresponding ellipses in the w-plane, and then sampling some points of z and connecting them to their corresponding points of w with straight lines. Notice that as the horizontal lines (in the bottom) are further away from iy=0 (the center line), the corresponding ellipses become rounder and rounder. As the horizontal lines are closer to iy=0, the corresponding ellipses are thinner and thinner. The focus of all the ellipses in the w-plane is (-1, 0) and (1, 0). Playing around with the model and adding some random thoughts in the modeling I got this shape that I like a lot! I named it: Light Tower. I placed it next to my scented candle, and with the LED lights added on, it creates a perfect decoration that makes a romantic / nice atmosphere at night! ***** I ordered my model to be printed from Shapeways.com. This model is only 10cm tall, about 6.7cm long and wide. It is so small and therefore very delicate. You need to handle it with care as it can easily break. You can scale it up for a bigger and stronger print if you want, but it could get expensive! LOL (Because this small model cost me about 30 US dollars to print from Shapeways!) ***** The LED light strip I used is ordered on Amazon.com: https://www.amazon.com/gp/product/B013TEEKOK/ref=oh_aui_detailpage_o06_s00?ie=UTF8&psc=1 There are lots of other LED light strip options that you can try out though! Some have different colors, some would blink, etc..