8000 GitHub - dnshkmr7/complex-fibonacci: Visualization of the Fibonacci function extended to complex inputs. Discussed in the Stand-up Maths video. https://youtu.be/ghxQA3vvhsk
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Binet Formula Visualization

A 4D visualization of the Fibonacci function extended to complex inputs using Binet Formula, inspired by the Stand-up Maths video. The interactive plot can be found here.

This project visualizes:

  • x & y axis represent real and imaginary parts of a complex number.
  • z axes & colorbar represent real and imaginary parts of the Fibonacci function evaluated at that complex number.

Binet Formula (Extended to Complex Inputs)

$$ F(z) = \frac{\phi^z - \psi^z}{\sqrt{5}} $$

$$ \phi = \frac{1 + \sqrt{5}}{2}, \quad \psi = \frac{1 - \sqrt{5}}{2}, \quad z = x + iy $$

Scaling

To keep the visualization both smooth and pretty, especially for large oscillating values I apply the inverse hyperbolic sine function on the real and imaginary parts of the result.

$$ \sin^{-1}h(x) = \ln\left(x + \sqrt{x^2 + 1}\right) $$


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Visualization of the Fibonacci function extended to complex inputs. Discussed in the Stand-up Maths video. https://youtu.be/ghxQA3vvhsk

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