Saint Jerome as a mathematical expression

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Iterative Experiment with Complex Formulas

Introduction:
In this exploration, we're experimenting with complex numbers using two distinct mathematical operations. The idea is to see what patterns emerge when we apply these operations repeatedly, starting from different random points each time.

Methodology:

Formulas:

The first operation transforms a number by raising it to the fourth power and then adding a constant (which is also a complex number).
The second operation transforms a number by raising it to the fifth power and then adding the same constant.
Initial Setup:

We repeat the entire process 23 times.
In each repetition, we perform 2048 iterations, keeping track of the results.
Execution:

Starting Point:
Each repetition begins with a random complex number. This number is used as the starting point for both operations.
Constant Selection:
A separate random complex number is chosen for each repetition and is used as the constant in both operations.
Iterative Process:

In each of the 2048 iterations per repetition, we:
Apply the first operation (raising to the fourth power and adding the constant) to the current number.
Apply the second operation (raising to the seventh power and adding the constant) to the current number.
After the iterations, we divide the result of the second operation by the result of the first operation and store this quotient.
Repetition:

This entire process is repeated 23 times, with new random starting points and constants each time.
Data Analysis and Visualization:

After completing all repetitions, we plot these stored quotients on a complex plane. This helps us visualize the relationships and patterns formed by the operations.
Conclusion:
This experiment offers a unique look into the behaviors of complex numbers under iterative operations. The randomness in the starting points and constants helps reveal diverse and intricate patterns, highlighting the fascinating nature of complex calculations.

Code:https://pastebin.com/x3A0tNB7