Wien's peak: λ_max = b/T, b = 2.898×10⁻³ m·K Stefan-Boltzmann: P = σT⁴ (σ = 5.670×10⁻⁸ W/m²K⁴)
The photons below are emitted with a colour drawn at random from the true
Planck distribution at this temperature (inverse-CDF sampling) — their colour
mix is exactly the shape of the curve above, not a fake gradient.
About the 2D Blackbody Radiation Visualiser
This 2D companion plots the same Planck radiation law as the 3D version — B(λ,T) = (2hc²/λ⁵) · 1/(e^(hc/λkT) − 1) — but adds a live particle system: photons are emitted at random wavelengths drawn from the actual spectral distribution at the current temperature (inverse-CDF sampling over the discretised curve), so the mix of colours streaming across the canvas is not an artistic gradient but a direct visualisation of the probability density itself.
The colour swatch is computed the same way in aggregate: the curve is integrated across the visible band (380–750 nm), each sample weighted by an approximate wavelength-to-RGB response, and the result normalised to full brightness — so the swatch genuinely shifts from deep red, through white, to blue-white as temperature rises, exactly tracking the physics rather than a canned lookup table.
Frequently Asked Questions
How is the peak wavelength verified?
Two independent numbers are shown: Wien's law λ_max = b/T (an analytic formula), and the wavelength at which the sampled Planck curve numerically reaches its maximum value. They agree to within the resolution of the sampling grid, which is a direct on-page check that the plotted curve really is Planck's law rather than a decorative approximation.
Why do the photon colours change as temperature rises?
Each photon's colour is sampled from the true Planck probability distribution at that temperature. At low temperature the distribution is concentrated in the infrared, so photons render as encoded near-red before dropping below the visible cutoff; at high temperature the distribution shifts toward blue and ultraviolet, so more visible photons appear blue-white.
What does the total power readout mean?
It is the Stefan-Boltzmann total radiated power per unit area, P = σT⁴, integrated over all wavelengths (not just the visible band). It grows with the fourth power of temperature — doubling T multiplies the emitted power by 16.