Rendered on turbowarp, the zoom stopped here because the frames would not stay in order as I was saving them to a folder, though I wouldn't have made it much further anyway considering that floating point errors destroy the set past a point that is just a bit closer than this. If you don't want to read this, see this project!! https://scratch.mit.edu/projects/978730010/ The Mandelbrot set is a shape that arises from a complex function called "Z = Z^2 + C", don't be fooled by its apparent simplicity, the function itself has a little bit more complexity than that, because Z actually represents 2 values: Z real and Z imaginary. Z real is the result of squaring the x coordinate (0-1, I divided x and y by 240 and 180 respectively), squaring the y coordinate, then after squaring the 2 values you will get 2 new resulting values. The next step is to take the resulting value of Y from the resulting value of X, and adding C real to the result of doing this, which is simply the x coordinate. Z imaginary is created by getting the x coordinate, and the y coordinate, multiplying them together (x*y rather than x*x minus y*y) multiplying the result by 2 (2(x*y)), and adding C imaginary which is... what a surprise, It's the y coordinate! Then 2 values also called X and Y are created, and store the result of Z real and Z imaginary respectively. The next step is to use the values of X and Y, replacing the x and y coordinates with these values, effectively plugging Z back into the equation, getting the result, and replacing the values of the variables X and Y with the result. do this a lot of times over an area such as this and you get a lot of values, if you make the X position be Z real and the Y position be Z imaginary, you will see that the point has moved elsewhere, and you can check the distance from the center, using the complex looking equation "sqrt(x^2 + y^2)", which is created by the same logic as A^2 + B^2 = C^2, where multiplying A and B by themselves and adding them together will give you the same result as multiplying the distance by itself. If it's greater than 2, then that point is going to keep getting further away and can be ignored, If it's still less than 2, you can assume it's going to stay within the circle. For those who still don't understand, check out this project: https://scratch.mit.edu/projects/978730010/ #trending #art #animation #trending #art #animation #trending #art #animation #trending #art #animation #trending #art #animation #trending #art #animation #trending #art #animation #trending #art #animation #trending #art #animation #trending #art #animation #trending #art #animation #trending #art #animation
Iterations: 450 Real coordinates (x offset): -1.76801020788529248509645593250143145278780861966542863068817686693288089075260813052330270823522588000592308431833 Imaginary coordinates (y offset): -0.00654973441367893105006607760099556478255787170697712574921822035432228058759401017968619999359685041497712583277 Final zoom: 91377.74 (Manually rounded, the value is still pretty precise here)
