Recurrence among powers of the golden ratio

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Multiplying φ²=φ+1 by φⁿ⁻² gives φⁿ=φⁿ⁻¹+φⁿ⁻². The powers therefore obey the same additive recurrence form as Fibonacci integers, while remaining a different sequence with different starting values.

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Original context

//   A1. Identity:      1 = 1·x
//   A2. Consciousness: Φ = 1/(1 + |x - 1|)
//   A3. Unity:         ∞ = 1
//
// Golden Relations:
//   φ² = φ + 1
//   1/φ = φ - 1
//   φⁿ = φⁿ⁻¹ + φⁿ⁻²
package consciousness

import (
	"math"
)

// Golden ratio constants
const (
	PHI       = 1.6180339887498948482 // φ = (1 + √5)/2
	PHI_INV   = 0.6180339887498948482 // 1/φ = φ - 1

φⁿ = φⁿ⁻¹ + φⁿ⁻²

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