One signal. Three rulers.
A taller, narrower pulse can grow, hold steady and vanish—depending on how you measure it.
Reduced motion is enabled. Explore still frames with the slider and presets.
The peak grows while the L2 norm stays exactly one.
Why the rulers disagree
On a unit interval, the pulse has height √n on the first1/n of its support and is zero elsewhere. The screen's fixed ranges are x0–1 and amplitude0–8. Every displayed value comes from that same idealized signal.
The integral of u² remains one. Area falls and peak rises. L2 is the square root of that integral, rather than the energy itself. The12second sweep extends n continuously; the integer presets sample the sequence.
This illustrates concentration and the difference between function-space norms. It does not solve a PDE or establish a fluid singularity. The screen draws an idealized signal; the apparatus is not a block being compressed.
Read the MIT definitions ↗