Mandelbrot coordinates to Julia set

Question

I was working on a Mandelbrot set at first, then added a Julia set to the same window. The problem is I don't know the formula for my exact situation. Also, the Julia set slid to the bottom-left side. The issue is that it's not taking into account the zoom factor and the x, y offsets, and (for some reason) only accounting the bottom left square like 50 by 100 pixels. Here's my code and formula:

fractal image with the julia set missplaced:

$fractal image with the julia set missplaced$

zx = ((mouse.x / 800.0 - 0.5) / (1 / mandelbrot.get_zoom_scale())) * 6 - mandelbrot.get_x_offset() - 3.5;
zy = ((mouse.y / 600.0 - 0.5) / (1 / mandelbrot.get_zoom_scale())) * 6 - mandelbrot.get_y_offset() - 2.5;

The constructor of the class that handles all the fractals has these parameters:

FractalBase<Derived>::FractalBase()
    : max_iterations(300), basic_zoom_x(240.0f), basic_zoom_y(240.0f),
    zoom_x(basic_zoom_x), zoom_y(basic_zoom_y),
    x_offset(3.5f), y_offset(2.5f),
    zoom_factor(1.0f), zoom_speed(0.1f),
    pixels(new unsigned char[width * height * 4]), paletteSize(palette.size()),
    zoom_scale(1.0f), width(400), height(300)

So, the main problem is that it miscalculates the zx and zy parameters, not including the zoom_factor, and not accounting for the offsets. I tried a lot of different functions but just couldn't find the one that will actually work. I would like assistance with the formula.

Why use double math as in mouse.x / 800.0 ..., yet float math elsewhere? — chux
– chux, Commented Mar 22 at 17:18
The mouse variable is just sf::Vector2i, means it contains 2 integer values representing positioning of the mouse in the window in pixels, and as you can tell, it just have 2 integer numbers inside, so if you don't cast to the flooring number one of those, it will divide incorrectly — NeKon
– NeKon, Commented Mar 22 at 17:35
"... if you don't cast to the flooring number" is not the issue. Why use double when rest of code uses float? Mandelbrot's are sensitive to that sort of thing. I do not know it it makes a difference for you issue, just trying to understand why your code uses a mixture of FP types. I'd consider using double or float everywhere. — chux
– chux, Commented Mar 22 at 18:11
it may be, but the problem happens only with the julia set, cause with mandelbrot zoom and drag worked fine, it is the formula to convert to z exactly that causes an issue — NeKon
– NeKon, Commented Mar 22 at 18:58
i am like 100 percent sure it is the formula (zx, zy) problem, the actual Julia set formula works fine, but the conversion to zx and zy - that's the problem — NeKon
– NeKon, Commented Mar 22 at 19:05

NeKon · Accepted Answer · 2025-03-23 12:29:09Z

2

so after a lot of trial and error and hours spent, here is the correct formula, so many hours spent on a simple formula, but it gave me so much dofamine when it started working

zx = -(mandelbrot.get_x_offset() - (mouse.x / mandelbrot.get_zoom_x()));

zy = -(mandelbrot.get_y_offset() - (mouse.y / mandelbrot.get_zoom_y()));

answered Mar 23 at 12:29

NeKon

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