# Newton Basin Project

### Open Source Your Knowledge, Become a Contributor

Technology knowledge has to be shared and made accessible for free. Join the movement.

## Here is a slightly more interesting output

Note that u here is the Heaviside step function but it's applied to the (shifted) modulus of a function rather than a variable. That is, we are interested in roots of g(z;k)≡f(z)+u(|f(z)|−k−1)kSin(z). This will yield the same roots as f(z)=x3−x on the real line. This obtains from Rouché's theorem as long as |f|<k, sin(z) being of bounded modulus there. Elsewhere the value can be seen as depending on the hyperbolic sine of the imaginary part of z, sinh(ℑz). Proof of which.

Suggested playgrounds

Open Source Your Knowledge: become a Contributor and help others learn. Create New Content