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I've written a package that allows you to easily generate images of self-similar sets in the plane. Here is a zip file containing that package, as well as a related package for digraph self-similar sets. Here's an example of its use that seems related to your needs. We first load the package, after placing it in our $Path, as described in the installation ...


6

Another way to zoom around is using Manipulate. Here we use a 2D slider to set the position and a regular slider to set the zoom. It scrolls more evenly if you hold down the option key as you move the sliders. Manipulate[b = -Log[a]; MandelbrotSetPlot[{u[[1]] + u[[2]] I - b - b I, u[[1]] + u[[2]] I + b + b I}, MaxIterations -> 200], {{a, 0.50, ...


18

Quick&Dirty: pt = {0, 0}; full = MandelbrotSetPlot[]; r = 0.2; Column[{ Row[{"Zoom: ", Slider[Dynamic[r], {0.01, 1}]}], Row[ { LocatorPane[Dynamic[pt], Dynamic[Show[full, Graphics[{EdgeForm[Red], Transparent, Rectangle[pt + r, pt - r]}], ImageSize -> Scaled[.45]]]], Dynamic[ MandelbrotSetPlot[{pt + r, ...



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