Is the 'Fibonacci sequence' the same as the 'Mandelbrot set'?

No. Actually, these two are not even remotely related.

The Fibonacci sequence is a sequence of whole numbers.It starts with 1, 1 and then each further element is the sum of the previous two: 1+1=2, 1+2=3, 2+3=5, 3+5=8. After that, it continues 13, 21, 34, 55, 89...

The Mandelbrot set is based on complex numbers, x+iy, with i being the square root of -1. You choose any c, then repeatedly calculate z'=z²+c, starting with z=0. If this sequence never goes infinite, c is a member of the set, otherwise it is not.

It has the weird property that sometimes two numbers very close to each other can both be part of the set, but the average of those two is not - the boundary of the set is not smooth, but a so-called fractal.

https://en.wikipedia.org/wiki/Fibonacci_sequence
https://en.wikipedia.org/wiki/Mandelbrot_set

As a side note to WesleyCrusher; Madelbrot's and Fractal's were seen as early computer graphic art..

https://www.fountainware.com/Funware/Mandelbrot3D/Mandelbrot3d.htm