Fun math art (pictures) - benice equation

Let f(a,b,x,y) = 1/exp(1/(a² - x²)²) + 1/exp(1/(a² - y²)²) - b Equations: Blue grid (#) ..... f(2, 0.999, x, y) = 0 Green noug...

(1) Archimedean spiral (2) Fermat's spiral (Parabolic spiral) (3) Hyperbolic spiral (Reciprocal spiral) (...

Spiral Types: (1) Archimedean spiral: r(θ) = a*θ (1 < number of spiral turns < 2) (2 < number of spiral turns < 3)...

Spirals (green, magenta) around a Spiral Dodecaskelion (grey) (GIF animation) A spiral of spirals of spirals. The spirals are...

The spirals are logarithmic spirals: r(θ) = a exp(bθ), b = 0.25. The spirals are logarithmic spirals: r(θ) = a exp(bθ), b ...

A pentaskelion with five logarithmic spirals r(θ) = a*exp(b*θ), b ~ 0.30635 (same as that of the golden spiral). b = 0.25 b =...

( Monster ) ( Funny Face ) ( Monkey Face ) ( Mathematical software used: Graph )