New fractal family with K-parameterised area-decay classification
Mike Bird
SeqFan,
I’d like to share a new fractal family and an associated area-decay classification that may be of interest.
The Aether Set is defined by the non-holomorphic iteration z_{n+1} = K·z_n·g(Im(z_n)) + c, z_0=0, with escape radius R=10. For g(y)=e^y and K=2^N−1, this arises as the stability boundary of a multi-agent intelligence metric. The set is distinct from Mandelbrot/Multibrot/Burning Ship families by a key property: it forms a K-parameterised family — geometrically distinct but structurally related fractals, one per integer K — with double self-similarity both within fixed K and across the K-family.
The main result: for any g with g(0)>0 (Class A), the stable area satisfies A(K) ~ (π R²/g(0)²)·K⁻², giving γ=2 universally. For g(0)=0 with a first-order zero (Class B, e.g. tanh), γ=1. The general formula is γ=2/(1+α) where α is the order of the zero of g at the operating point. This classification has no known analogue in Mandelbrot, Multibrot, or Burning Ship literature.
The integer sequence K²·A(K) converges to π·R² ≈ 314 (Class A) or K·A(K) → 211.65 (Class B, R=10). The ratio 211.65/π ≈ 67.36… does not appear in OEIS.
Preprint (Zenodo): https://doi.org/10.5281/zenodo.19101554
Is the γ=2/(1+α) classification, or the constant C_B ≈ 211.65 for Class B, known in any related fractal literature?
~Michael Bird, Independent Researcher, Reno NV
Michel Marcus
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Mike Bird
Apologies for the formatting — fixed below.
Is the γ = 2/(1+α) area-decay classification, or the constant C_B ≈ 211.65 for Class B, known in any related fractal literature?
Context: non-holomorphic iteration z_{n+1} = K·z_n·g(Im(z_n)) + c, K-parameterised family with double self-similarity. Preprint: https://doi.org/10.5281/zenodo.19101554
—Michael Bird, Independent Researcher, Reno NV
Joerg Arndt
This is a case of "Not even wrong".
The submissions (and the zenodo preprints) may superficially resemble scientific publications
but absolutely drown in jargon and non-sequiturs.
Already in the abstract your mention "Grok AI". Using AIs for purposes of creating OEIS sequences
is discussed at https://oeis.org/wiki/Use_of_AI_for_OEIS_Submissions
In short: don't use AI.
It is exceedingly unlikely any OEIS editor will spend time reverse engineering what you
may have had in mind.
Some other problems, already sufficient for rejection, where given as "pink-box" comments
with your submissions.
Best regards, Joerg Arndt
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