### Lambert W function

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#### superheal

• Fractal Fanatic
• Posts: 27

#### Lambert W function

« on: September 10, 2018, 07:00:06 PM »
Hi,

as I was exploring the solutions of the Lambert function (z*e^z = c), I used newton's method to visualize them.
z = z - (z*e^z - c) / ((z + 1)*e^z)
It produced some nice images but then I started playing with the original function.

I tested z*e^(z^2) = c,
z = z - (z*e^(z^2) - c) / ((e^(z^2)) * (2*z^2 + 1))

and voila, I got some mandel minis too!

#### v

• Fractal Fanatic
• Posts: 31

#### Re: Lambert W function

« Reply #1 on: October 31, 2018, 02:55:40 AM »
really nice fractal and idea, amazing to see a minibrot in the newton fractal style pattern.  are you using escape time for rendering the fractals with the e^z and e^z^2 terms?

#### superheal

• Fractal Fanatic
• Posts: 27

#### Re: Lambert W function

« Reply #2 on: December 03, 2018, 09:44:54 PM »
Yes, I am using escape time, but obviously for a convergent fractal. norm(z - z_prev) <= epsilon

• Posts: 171

#### Re: Lambert W function

« Reply #3 on: December 06, 2018, 05:38:25 AM »
Suggestion - try it inverted with divergent bailout.....

z = ((e^(z^2)) * (2*z^2 + 1)) / [z*((e^(z^2)) * (2*z^2 + 1)) - (z*e^(z^2) - c)]

if that doesn't produce anything interesting then maybe raise a power by 1 on the top e.g. e^(z^2+1) or 2*z^3+1
The meaning and purpose of life is to give life purpose and meaning.

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