continu.ax

the unbroken line

(1, 4)

Continuity

Between any two points on a continuous function, there exists a path. No gaps, no jumps, no sudden departures from the trajectory. The curve knows where it has been and where it is going. This is the fundamental promise of continuity: the guarantee that small changes in input produce small changes in output.

The domain name itself is an axis -- continu.ax -- a coordinate system for continuous thought. Every scroll reveals more of the curve, more of the story, more of the unbroken line that connects origin to infinity.

(3, -2)

Inflection

At the inflection point, the curve changes its mind. Concavity flips -- what was bowing upward begins to bow downward, or vice versa. The second derivative crosses zero. It is the moment of transformation, the pivot where acceleration becomes deceleration.

In design, as in mathematics, inflection points are where the interesting things happen. The transition from light to dark on this page is an inflection -- the function crosses the axis, the background inverts, and the narrative shifts register.

(5, 1)

Frequency

Rapid oscillations encode dense information. Each peak and trough carries a quantum of meaning, compressed into tight wavelengths.

(6, -1)

Amplitude

The height of each wave determines its energy. Large amplitudes demand attention; small ones whisper at the threshold of perception.

(7, 0.5)

Phase

Two waves, identical in frequency and amplitude, can cancel each other if their phases oppose. Alignment is everything.

(9, 0.1)

Convergence

The oscillations dampen. Energy dissipates into the medium. The curve smooths, approaching its limit with asymptotic patience -- each increment of scroll bringing it closer but never arriving. This is the nature of limits: the destination exists in theory but not in practice. The journey is the continuous function; the limit is its meaning.

continu.ax