by Kayiilu

Inspired by an applied complex variables class! :D

Specifically, 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 naive 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 draw horizontal lines on the z-plane and corresponding ellipses in the w-plane, and then sample some points of z and connect 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 are (-1, 0) and (1, 0).

Playing around with the model and add some random thoughts in the modeling I got this shape that I like a lot!

I named it: Light Tower.
I put it next to my scented candle, and with the LED lights added on, it is 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 of length and width.
It is so small and therefore very delicate. It is easy to break so you need to be careful handling it.
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..