Kardashev scale. Nikolai Kardashev (1964) classed civilisations by the power they command. Sagan's continuous version is K = (log₁₀P − 6)/10 with P in watts, which puts Type I at 10¹⁶ W, Type II at 10²⁶ W and Type III at 10³⁶ W. Other conventions differ: the planet's intercepted sunlight is πR²S ≈ 1.7×10¹⁷ W, the Sun's luminosity is 3.83×10²⁶ W, and Kardashev's own numbers were 4×10¹², 4×10²⁶ and 4×10³⁷ W. The selector in the Growth tab switches between them.
Humanity today. Primary energy use is of the order of 2×10¹³ W (roughly 600 EJ per year), so K ≈ 0.73. This is an order-of-magnitude figure from public energy statistics, not a precise number.
Growth. Exponential growth P(t) = P₀ e^(rt) reaches P at t = ln(P/P₀)/r. At 2 %/yr this is about 450 years to the planet's sunlight and about 1530 years to the whole Sun. Nothing guarantees such growth; a logistic curve P = Pmax / (1 + (Pmax/P₀ − 1) e^(−rt)) saturates at a cap. Sustained 2 %/yr growth is a thought experiment, and the lab shows both so the limits are visible.
Dyson swarm. Freeman Dyson (1960) pointed out that a civilisation could intercept a star's output with a cloud of independent collectors (a rigid shell is mechanically unstable). Collectors needed: N = f · 4πr² / A. Mass of the film: m = f · 4πr² · d · ρ. At 1 AU with a 1 µm aluminium film this is about 7.6×10²⁰ kg (about 0.8 Ceres masses, 0.2 % of Mercury); a 1 mm structure would already need about 2.3 Mercury masses. Armstrong & Sandberg (2013) discuss taking the material from Mercury. The simulator draws about 6000 instanced collectors as a schematic: real counts are 10¹⁶ to 10²⁵.
Waste heat. Energy is conserved, so every watt used is eventually radiated. A surface at distance r from a star of luminosity L absorbs flux S = L/(4πr²) and radiates from n faces: αS = n ε σ T⁴. For a complete shell (n = 1, α = 1) this is T = (L / (4πσr²ε))^(1/4), 394 K at 1 AU for ε = 1; thin free collectors radiating from two faces reach 331 K. The peak wavelength is λ = b/T (Wien, b = 2.898 mm·K), about 7 µm: a mid-infrared source, which is how Dyson, and later Wright et al. (2014, Glimpse/G-HAT searches), proposed to look for such structures. Temperature does not depend on the covered fraction of a thin swarm because absorbed power and radiating area scale together. The infrared spectrum drawn here is a single-temperature greybody, not a measured one.
Landauer limit. Erasing one bit costs at least E = kB T ln 2 (Landauer 1961; the bound was measured by Bérut et al., 2012). At 300 K that is 2.9×10²¹ J. Dividing the available power by E gives an upper bound on irreversible bit operations per second. Today's chips use many orders of magnitude more per operation; the slider shows the headroom. Reversible computing can in principle go below the bound.
Fermi paradox, one line. If energy-hungry civilisations were common and grew like this, some should be visible as infrared excesses, yet none has been confirmed, which is part of the puzzle.
Simplifications. A single star of constant luminosity; no stellar evolution; the swarm is spherical and static in the thermal model; no orbital dynamics of the collectors; no efficiency limit beyond the slider; growth rates are assumptions, not forecasts.