Complex Fibonacci - Part 1

What happens to Fibonacci Numbers and related sequences in the Complex realm? In this two part exploration, we'll look into the characteristic shapes and properties of generalized sequences created by adding two previous elements.

00:00 Intro
00:56 Fibonacci and Lucas Numbers in Reverse
03:54 Drawing Sequences Parametrically
06:04 Generalizing Fibonacci Sequences
08:17 Shapes of Fibonacci Curves
11:42 The ψ Spiral
13:32 Resources for Play
14:49 Outro

Previous video, detailing how we find the closed-forms we start with:
   • Golden Threeway - Fibonacci, Lucas and the...  

Desmos graph for trying it yourself:
https://www.desmos.com/calculator/ppp...

NOTES:
The closed-form formulas explored here get multivalued for non-integer inputs of n, and we are only considering the principal branch
A Golden Spiral is a logarithmic spiral that grows by a factor of Φ every quarter-turn. The shape of continuous ψ powers in the Complex Plane is a spiral that grows by a factor of Φ every half-turn.