File:Complex Fibonacci Spiral with Positive and Negative Binet Variations.gif
Summary
| Description |
English: Animated turnaround of a 3D plot of Binet's formula F(n) = (ϕ^n − ψ^n) / (ϕ − ψ) for the Fibonacci Sequence with real-number input n on the x-axis, the real component of the output on the y-axis, and the imaginary component of the output on the z-axis. Also shown are three variations on Binet's formula: Fa(n) = ϕ^n / (ϕ − ψ), which rounds to the nth Fibonacci number for positive integer values of n; Fo(n) = (ϕ^n + (−ψ)^n) / (ϕ − ψ), which gives the nth Fibonacci number for odd integer values of n; and Fe(n) = (ϕ^n − (−ψ)^n) / (ϕ − ψ), which gives the nth Fibonacci number for even integer values of n. |
| Date | |
| Source | Own work |
| Author | ztlawton |
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