Daisyworld - 3D

What Daisyworld is. A thought-experiment planet by Andrew Watson and James Lovelock (1983) that shows how life can regulate its own climate without planning. The surface is bare ground (albedo A_g = 0.5) plus two kinds of daisies: white (A_w = 0.75, reflect light, cool the patch) and black (A_b = 0.25, absorb light, warm the patch). The planet's albedo is the area-weighted mean:

Energy balance. The planet radiates what it absorbs. With the model's flux constant S = 917 W/m² (the 1983 paper's value, already a disk-averaged number) and star luminosity L relative to today:

Patches are not exactly at the planet mean. A patch with albedo A_i is warmer or cooler by a linear-in-T⁴ rule, where q = 2.06×10⁹ K⁴ sets how poorly heat moves between patches:

Growth and death. Daisies grow best at an optimum temperature (22.5 °C) and not at all below 5 °C or above 40 °C. The parabolic growth rate and the population equation are:

New daisies can only grow on bare ground (the factor α_g); γ = 0.3 is the death rate. A small seed refuge keeps each type from dropping to exactly zero so it can come back.

Why it regulates. When the star is dim, black daisies are warmer than the planet and win; they darken the planet and warm it. As the star brightens, white daisies take over, brighten the planet and cool it. Between L about 0.72 and 1.5 the living planet stays within 5 °C of the optimum, while the same planet without daisies is only comfortable for L from about 0.88 to 1.01. At the high-L end the daisies suddenly die and the temperature jumps up; ramping L back down shows a hysteresis loop (dashed curve in the third graph).

Numerical checks run on this page. (1) The bare planet is compared with the closed-form Stefan-Boltzmann temperature. (2) A white-only world is integrated as an ODE (fourth-order Runge-Kutta) and compared with an independent root-find, bisection on (1 − α)β(T_w(α)) = γ. (3) The radiation bookkeeping ∑ α_i T_i⁴ = T_e⁴ is verified for the current state.

Honest simplifications. Daisyworld is a deliberately minimal toy, not a prediction of Earth's climate: no atmosphere, no greenhouse effect, no seasons, no oceans, no spatial heat flow other than the single parameter q, and no evolution. The star's luminosity is a free slider, and the luminosity range is far wider than the Sun's real brightening (about 1 % per 100 million years). The spatial daisy pattern shown on the planet is a visual device: a fixed random field decides which spots turn white or black, so that the area fractions drawn are exactly the model's fractions. The Daisyworld idea is a model of feedback, and the Gaia hypothesis it was created to illustrate is still debated.