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Generalized Collatz Fractals
Visualize the hidden mathematical structures within generalized Collatz sequences. These fractals emerge from a simple iterative process, revealing the elegant boundary between order and chaos.
Generalized Collatz Function:
f(n) = {
n/Y, if n ≡ 0 (mod Y)
(n×(X+1) + (X-r))/Y, otherwise
}
where r = n mod X, and X = Z^m
f(n) = {
n/Y, if n ≡ 0 (mod Y)
(n×(X+1) + (X-r))/Y, otherwise
}
where r = n mod X, and X = Z^m
Use manual input fields to explore extreme parameter ranges beyond slider limits. The live preview shows real-time changes, while the full canvas provides maximum detail.