Prometheus signature: logistic map at r=3.8

Read the equation

The function returns 3.8x(1−x). On [0,1] it is nonnegative with maximum 0.95 at x=0.5, so that interval maps into itself under the isolated recurrence. The network supplies a sine input, which can be negative; the familiar [0,1] logistic-map behavior does not automatically apply to those inputs.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

// FHephaestus: F_Hephaestus(x) = ∫∫ K(x,y) dy dx (Engineering - double integral)
func FHephaestus(x float64) float64 {
	// Simplified: K(x,y) = xy, ∫∫ xy dy dx from 0 to x
	// = ∫ x·(x²/2) dx = x⁴/8
	return math.Pow(x, 4) / 8.0
}

// FPrometheus: F_Prometheus(x) = x·(1-x)·r (Innovation - logistic map)
func FPrometheus(x float64) float64 {
	r := 3.8 // Chaotic regime
	return r * x * (1.0 - x)
}

// FDionysus: F_Dionysus(x) = e^{iωt}·A(x) (Creativity - complex exponential)
func FDionysus(x float64) float64 {
	// Return magnitude of creative oscillation
	omega := 2.0 * math.Pi / BasePairsPerTurn
	c := cmplx.Exp(complex(0, omega*x)) * complex(math.Sin(x), 0)

FPrometheus: F_Prometheus(x) = x·(1-x)·r (Innovation - logistic map)

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