Set of fractal needed

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I am preparing for some cognitive study. For one of the experiment I need to produce a set of fractal pictures (10-30 pictures). For study consistence these fractals should belong to one class (from mathematical point of view), Should share some common features, but be visually distinguishable. So, in other words, I am searching for fractals, which are like dogs types: looks very different, but everybody absolutely sure, that they belong to one species.

Could you give me advice which fractals I may try?

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Julia set (which depends on a complex constant) and Newton fractal (which depends on a polynomial) immediately come to mind.

I wonder what kind of study are you doing.