Fibonacci numbers, Lucas numbers and related sequences can be modified to start not just with integers or Real numbers, but also with Complex numbers. What kinds of shapes will they trace in the Complex Plane when we draw them continuously? And what if we plug Complex numbers into the factors of the preceding elements as we add them? Or even into the index of the sequence?
00:00 Intro
00:44 Defining Seeds
03:00 Lucas and Fibonacci Running Together
07:29 Finding the Hidden Sequence
12:09 Beyond the Principal Shape
13:24 Cycles!
17:53 General Closed Form
21:50 Cycles, But Continuous
23:08 Sticking Complex Numbers in the Index
25:50 Shadows of Fibonacci
Part 1 of this video
https://youtu.be/HEe6FSsJddU
Golden Threeway - Fibonacci, Lucas and the Golden Ratio
https://youtu.be/K1kk8BFCbek
Desmos graph for the Real Lucas + Imaginary Fibonacci numbers:
https://www.desmos.com/calculator/rffcb2v6ch