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How would you zoom to an area, over a number of frames, by the same percentage of the current view each frame?

I’m a novice coder, and I wanted to code a Mandelbrot zoom. I’ve coded everything, but I can’t find how to zoom in. I found a specific area that has a minibrot in, so I want to create a gif zooming to that point.
I coded it to use the bottom left and top right points of the viewing plane to draw the part of the mandelbrot set in that area, and I have the same points for the minibrot, with the same aspect ratio. But I don’t know how to zoom to that area (by changing the x and y of each bounding point) over a set number of frames, so that it zooms in smoothly.