This 2D companion drives the identical per-dot physics as the 3D membrane-patch version — inverse-transform sampling of a truncated power-law dwell time and exponential dye photobleaching — but never renders a spatial scene. Instead it displays three data-native views of the same random process: a scrolling telegraph trace (one row per quantum dot, one column per instant — bright = ON, dark = OFF), a live log-log dwell-time survival plot that accumulates every completed ON/OFF dwell across the whole ensemble and compares it against the exact analytic survival curve, and a strip chart of ensemble-averaged signal and dye brightness over time.
P(τ_on) ∝ τ_on^(−α) for τ_min ≤ τ_on ≤ τ_max
P(τ_off) ∝ τ_off^(−α) for τ_min ≤ τ_off ≤ τ_max
u ~ Uniform(0,1)
τ = ( τ_min^(1−α) + u·(τ_max^(1−α) − τ_min^(1−α)) )^(1/(1−α))
The dashed reference curve on the survival plot is not the naive asymptotic slope −(α−1) — over a finite truncation range (τ_min = 0.12 s, τ_max = 8 s, only ~67× apart) that approximation is measurably wrong. It is the exact truncated-power-law survival function derived from the same normalized density used by the sampler above:
S(τ) = (τ^(1−α) − τ_max^(1−α)) / (τ_min^(1−α) − τ_max^(1−α))
The organic-dye control population still decays smoothly and irreversibly:
I_dye(t) = I₀ · exp(−k·I_exc·t)
- Excitation intensity — scales the dye photobleaching rate constant and overall emitted brightness of both populations.
- Blink exponent α — reshapes the QD on/off dwell-time power law; higher α ⇒ shorter, more frequent switches, and a steeper survival-plot slope.
- Biomarker density — ensemble size; the telegraph trace visualizes up to 60 representative dots, but every readout and the survival statistics use the full simulated population.
- Time acceleration — compresses a multi-second imaging session into a few seconds of playback (it speeds up the underlying dwell-time kinetics, not the visual scroll rate of the trace).
Real-world relevance: single-molecule imaging papers routinely test the "blinking is a power law, not a Poisson process" claim with exactly this kind of log-log survival (or histogram) plot — a flat, straight line on log-log axes over a wide dynamic range is the fingerprint of scale-free intermittency, versus the sharply curving-down line a thresholded exponential process would produce.