[Mathematical Art] Light Tower

cults3d

Inspired by a challenging applied complex variables class. Specifically, inspired by w = sin(z), where z=x+iy, x and 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 it's impossible since it involves four dimensions - by setting the z-plane parallel to the w-plane. I then draw horizontal lines on the z-plane, corresponding ellipses in the w-plane, and sample points of z, connecting them to their matching points of w with straight lines. Notice that as the horizontal lines move further away from iy=0, the center line, the corresponding ellipses become increasingly rounder. Conversely, when the horizontal lines are closer to iy=0, the resulting ellipses in the w-plane become thinner and thinner. The focal point for all these ellipses is located at (-1, 0) and (1, 0). While playing around with this model, I incorporated some random thoughts during the modeling process, yielding a shape that I find particularly appealing. I've dubbed it: Light Tower. I positioned it next to my scented candle, complemented by LED lights, creating an ideal decoration for setting a romantic or pleasant atmosphere at night. I commissioned Shapeways.com to print my model. The finished product measures 10cm in height, approximately 6.7cm in length and width. Given its small size, it's extremely delicate, making it easy to break if handled carelessly. For a larger, more robust print, you can simply scale up the design - although this may come at an increased cost. My initial print from Shapeways came with a price tag of around 30 US dollars. For my LED light strip, I ordered the product from Amazon.com: https://www.amazon.com/gp/product/B013TEEKOK/ref=oh_aui_detailpage_o06_s00?ie=UTF8&psc=1 There are numerous other LED light strip options available on the market. Some come with different colors, while others feature blinking effects.