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DaisyBall, the Math

DaisyBall uses the same math described in
DaisyWorld - the Math, except:

- DaisyBall has 92 locations, to DaisyWorld's one. Each location has a separate
multi-species DaisyWorld calculation running. Each of the 92 locations is drawn with
one daisy on the ball.

- Since the base deathrate is 0.3, the petals of a daisy are colored based only on the
0.7 (70%) of daisies which could ever be alive. For example, if a 6-petaled daisy
represents a population of 30% barren, 45% black, and 25% white, it is drawn with
4 black petals and 2 white petals.

- The luminosity at each DaisyBall location depends on its latitude. The
planet is tilted at 23.5 degrees, which gives even the poles some light density.

- In order to use the same luminosity plot limits as DaisyWorld, the base albedos of black
and white daisies are 0.2 and 0.8, compared to DaisyWorld's 0.25 and 0.75.

- There are two kinds of insulation in DaisyBall - instrasite insulation between one color
population versus the multispecies location temperature, and planetary
insulation between the location and the world
temperature. DaisyWorld uses insulation of 0.12 between one-color population
and the planet (which is the single multi-color site). DaisyBall uses 0.12 for intrasite
insulation, and 0.3 for planetary insulation.

- Since DaisyBall has 2 orders of magnitude more work to do with all those parallel
DaisyWorlds running, it uses 2 orders of magnitude fewer convergence steps per luminosity step -
25, compared to DaisyWorld's 1000.

I don't believe typesetting the math here would help anyone understand it.

Please don't take the color names seriously - that's pure creative license. They
don't match the albedos of ground cover on Earth. Here are some actual terrestrial
albedo values:

Ground cover | Albedo |

deep water | .05 - .20 |

desert | .20 - .35 |

short greenery | .10 - .20 |

dry vegetation | .20 - .30 |

summer conifers | .10 - .15 |

deciduous forest | .15 - .25 |

snowy forest | .20 - .35 |

dry snow | .60 - .90 |

Cloud cover probably also varies up to 0.90 albedo.

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Further Information

Other help files: