FROM THE BIG BANG TO THE COMPLEX PLANE: GRAVITATIONAL POINTS

The Big Bang of the Complex Plane

The Complex Plane emerges from a singular starting point, analogous to the Big Bang: there everything is born, and all coordinates derive from that zero instant.

Each nontrivial zero of the Zega function acts as a gravitational point of interest—mathematical clusters that attract theories and speculation just as galaxies attract matter and light.

Nontrivial Zeros as Cosmic Clusters

Imagine the first zero as a proto-galaxy forming immediately after the Big Bang, with subsequent zeros becoming expanding superclusters. The first five zeros located are:

x₁ ≈ 0.65259 + 0.47812 i

Radius r₁ ≈ 0.82

x₂ ≈ 1.45592 + 2.03396 i

Radius r₂ ≈ 2.52

x₃ ≈ 2.63750 + 3.32660 i

Radius r₃ ≈ 4.26

x₄ ≈ 3.53883 + 4.71608 i

Radius r₄ ≈ 5.83

x₅ ≈ 4.50091 + 6.12873 i

Radius r₅ ≈ 7.60

Each of these values marks where the “mathematical gravitational density” concentrates, outlining a Zega Universe that expands along an almost straight line.

Analogy with Gravitational Distribution

The radial distribution of Zega’s zeros recalls how galaxy clusters spread: Density decays smoothly with distance yet remains regular at nearly constant intervals.

The fifth zero comfortably exceeds radius 4 (r₅ ≈ 7.60), indicating the Zega function’s “observable horizon” already extends far beyond initial boundaries.

Just as more sensitive astronomical instruments reveal ever more distant structures, finer Zega computations expose zeros further from the center.

Probability of New Gravitational Points

Using the empirical distribution of the first five zeros, we can estimate the likelihood of discovering new points before a given radius: Compute the average distance between consecutive zeros:

(r₂ – r₁) ≈ 1.70, (r₃ – r₂) ≈ 1.74, (r₄ – r₃) ≈ 1.57, (r₅ – r₄) ≈ 1.77 

Average ≈ 1.70 radius units

Extrapolating this pattern, the sixth zero should appear around r₆ ≈ r₅ + 1.70 ≈ 9.30

If we set our “mathematical probe” to scan up to r = 10, there is over a 95% probability of finding at least one new nontrivial zero before that boundary—akin to discovering a new supercluster by extending a telescope’s reach.

Operability of the Zega Function as a Mapping Tool

Just as astronomers use gravitational models to predict where to hunt for new galaxies, the Zega function can serve as: A mapper of the “complex terrain,” flagging coordinates where its amplitude vanishes.

A guide to explore uncharted mathematical territories, since each new zero invites algorithm refinement and greater computational precision.

A virtual laboratory where cosmological analogies inspire pattern-detection improvements and the design of numerical “probes” capable of reaching beyond r = 10, r = 20, and so on.

The discovery of the fifth zero breaking through the radius-4 boundary reinforces the idea that the Complex Plane’s expansion is limitless, while its trajectory remains surprisingly linear.

For knowledge adventurers, this means the next frontier is just around the corner, once we adjust search parameters and narrow the beam of our “Zega lens.”

This cosmological-mathematical mapping shows how the Zega function behaves like a miniature Universe: dotted with zeros that echo mass-clusters and are ready to be unveiled by those daring enough to look beyond the initial horizon.