# Harriet Fell

Tanabata is a Japanese star festival that celebrates the meeting of the deities Orihime and Hikoboshi. According to legend, the Milky Way separates these lovers, represented by the stars Vega and Altair respectively, and they are allowed to meet only once a year. (Wikipedia)

Thinking about the lovers wandering about the heavens and only occasionally coming near each other, I was reminded of images I had generated, many years ago, while studying moving roots of polynomials.

In these images, the drawing canvas is a region of the complex plane centered at 0+0i. Each point, z is lined up with a target point T = x+yi. A point z is then sent on a journey through its powers z^n until a power, z^n lines up again, as closely as possible with z and T. The value of n is used to assign a color to the point z. I see T as one of the lovers. The other lover z looks to T as it departs and, as it journeys, keeps looking back trying to get that same view of its lover.

Meeting: This is from my first series of images when the point T was fixed at (1, 0). The stars come together at last but for a brief moment and gentle touch.

The math4Tanabata2.html settings were T=(1, 0), colorA = red, colorB = dark green, gradient out with green component mod 2, N=32, epsilon=.2, width 4.

I cropped this to ¾ of its original height to emphasize the meeting forms.