Any mathematical problem that is NP-Hard and there is no known quantum computer speedup may be considered (currently) secure. However, note I said currently as the challenge today is we are in the infancy of understanding how to use quantum computers so assumptions today may not hold tomorrow. Mandelbrot and Julia Fractal sets are considered NP complete rather than NP Hard problems. However, here is an old paper that has a lot of background so this is not a new discussion! http://www.icsi.berkeley.edu/pubs/techreports/tr-90-058.pdf

Thank to Stephen Holmes for answering the question

Really I don't know

Really i dont know

Thank Andaloussi Issam and Bekzod Bekchanov

Mostly yes

Thank Shakir Tuleab

Sorry I don't know

Thank Tamara Alaa

Julia set fractals are normally generated by initializing a complex number z = x + yi where i2 = -1 and x and y are image pixel coordinates in the range of about -2 to 2. Then, z is repeatedly updated using: z = z2 + c where c is another complex number that gives a specific Julia set. After numerous iterations, if the magnitude of z is less than 2 we say that pixel is in the Julia set and color it accordingly. Performing this calculation for a whole grid of pixels gives a fractal image.

For the Mandelbrot set, c instead differs for each pixel and is x + yi, where x and y are the image coordinates (as was also used for the initial z value). The Mandelbrot set can be considered a map of all Julia sets because it uses a different c at each location, as if transforming from one Julia set to another across space.

http://www.karlsims.com/julia.html

Thank Len Leonid Mizrah for sharing useful information

Somewhat safe

Thank Shakir Tuleab

I am biochemist

But thanks it is intersting

Thank Rasha Shakir Nima

I think no.

Thank Dr Isam Alkhalifawi for sharing useful answer

A New Public-Key Cryptosystem Based on Mandelbrot and Julia Fractal Sets

Mohammad A Alia & Azman Samsudin

To some extent yes they are.

Thank dr Vincent O. Nyangaresi and Isam Alkhalifawi for answering the question

Mandelbrot set (Mc), in space of (z:=x+i*y) coordinate system, by sloving this equation after transfer sultion to pixels axis image we obtain Mc map and countors or images in classical processoers , while the quantum combination just will be after quantifying space of Z:=x+i*y

Thank dr Isamaldin Hassan Saeed Badawi for sharing useful answers

Let us go in logical direction for quntom computing by bits, the gate (transistor)of base is spin_ spin for electron, or photon , needs low temperature to decrease entropy of system, next is to backing and build quantum memeroy, and processe , nowadays no body do build quantum prosser as I know, many groups directed to DNA memories, thanks

Thank dr Isamaldin Hassan Saeed Badawi for sharing useful answer

Preprint The Universal Fractal Chirality of Riemann Zeta-Function: On...