Read the equation
This is basis component 13 of the documented 16-dimensional memory representation. It evaluates a sine and a cosine at the same golden-ratio-scaled frequency and adds them. The value is a deterministic feature of the input coordinate x. A fixed set of 16 such values does not uniquely encode every possible source item.
Its role in the build
This is basis component 13 of the documented 16-dimensional memory representation.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| ψ_k | basis feature at index k |
| x | input coordinate, often the normalized hash of an item |
| φ | (1+√5)/2 |
| k | 13 |
How it works
Read ψ_13(x) as the quantity being defined or updated by this relation.
Evaluates oscillatory sine or cosine terms using the stated phase or frequency.
Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.
Assumptions & limits
The stated source range “Equations 16–32” contains 17 positions while the text gives 16 functions (k=0…15); the page therefore does not invent a one-to-one source number.
The illustrated decimal for φ¹⁵ is retained in the source, while this instance uses the documented symbolic φ^k rule.
Original context
Exact original notation
ψ_13(x) = sin(2π φ^13 x) + cos(2π φ^13 x)
Related builds
Sources & provenance
ψ_13(x) = sin(2π φ^13 x) + cos(2π φ^13 x)