# 1.2: Daisyworld Game

## Parts Needed

Start with a 3x3 (or 5x5) board, a handful of black “daisies”, a handful of white “daisies”, D10 (digital) dice, and a (digital) record sheet. Also keep the tables below handy.

## Initial Conditions

• Assign one group member to record the temperature and the number of black daisies, white daisies, and empty squares for each turn.  Record the initial conditions in the Daisy World Record Sheet (link might not work for you, so here is a download and a printable version).
• Roll the D10 die to determine the initial temperature using the "Initial Temperature" table
• For each square on your board, roll the D10. Use your initial temperature and the “Daisy Sprouting Likelihood” table to populate the board with black daisies, white daisies and empty squares.

## Play

• Roll the D10 for each square on the board.  If the square is empty, use the “Daisy Sprouting Likelihood” table to determine what type of daisy (if any) sprouts in the square. Add a piece of that color to the square. If the square has a daisy in it, use the “Daisy Death Likelihood” table to determine whether or not to remove the piece from the square.

Option 1: Leave the square blank for this round

Option 2: Roll to see whether or not a new daisy sprouts

• Record the number of black daisies, white daisies, and empty squares in the record sheet.
• Calculate a new temperature using this formula (or use the spread sheet): $$T_{new} = T_{old} + c*(N_{black}-N_{white})$$

where:

$$T_{new} =$$ the temperature for the next round

$$T_{old} =$$ the temperature at the start of this round

c = a constant; you can choose the value of this constant. I recommend starting with c = 0.3

$$N_{black} =$$ the number of black daisies

$$N_{white} =$$ the number of white daisies

• Repeat using $$T_{new}$$.

## Tables

Die Role

1

2

3

4

5

6

7

8

9

10

Temperature

-2°C

2°C

7°C

12°C

17°C

22°C

27°C

32°C

37°C

42°C

### Daisy Sprouting Likelihood Table

No daisies sprout above 45°C or below -5°C. The letter in the table below represents the color of the daisy that sprouts. “-“ indicates that no daisy sprouts.

 Die Role Temperature 1 2 3 4 5 6 7 8 9 10 40.1-45°C - - - - - - - W W W 35.1-40°C - - - - W W W W W W 30.1-35°C - W W W W W W W W W 25.1-30°C W W W W W W W W W W 20.1-25°C B B W W W W W W W W 15.1-20°C B B B B B B B B W W 10.1-15°C B B B B B B B B B B 5.1-10°C B B B B B B B B B - 0.1-5°C B B B B B B - - - - -5-0°C B B B - - - - - - -

### Daisy Death Likelihood Table

If the die role is in the range shown in the table, the daisy dies.

 Daisy Color in Square Temperature Black White >40°C 1-10 1-5 35.1-40°C 1-10 1 30.1-35°C 1-8 1 25.1-30°C 1-5 1 20.1-25°C 1 1 15.1-20°C 1 1 10.1-15°C 1 1-5 5.1-10°C 1 1-8 0.1-5°C 1 1-10 -5-0°C 1-5 1-10 <-5°C 1-10 1-10

## Record Sheet

Group Name:

Initial Temperature:

Rules: _____Standard              _____Alternate (describe modifications)

 Black White Empty ΔT (°C) T (°C) 0