How to get a bigger mantissa in Python programming language?

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I'm trying to make an animation of Feigenbaum's chaos. I try to program 600 images where I dive into the chaos of the image and then make them animated with MakeAvi. I have an mpmath library from Python, but it still feels like the value of the 10 exponent mantissa is limited. I can't go beyond image 82, which is equivalent to 15 frames per second animation with only 82/15 = 6 second animation. How could I increase the magnitude of the floating point mantissa? I suspect the value of the mantissa is currently limited to about 300. So I'm trying to make an animation like this:

https://youtu.be/5cT0H4Xk7JE

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