-- card: 9239 from stack: in
-- bmap block id: 11425
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-- background id: 2811
-- name: 


-- part 2 (button)
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-- part name: x density
----- HyperTalk script -----
on mouseUp
  open "bin:quadratic map:x density"
end mouseUp



-- part contents for background part 22
----- text -----
For  3.569946 < a  we observe an  inverse cascade  
---although chaotic there exists much structure:

•  the chaotic intervals merge together until iterates cover all of  0 ≤ x ≤ 1  at  a=4  (sometimes, but inaccurately, called "inverse bifurcations");

•  there exist many windows of periodic behaviour characterised by stable  p-cycles with associated period-doubling cascade  (p, 2p, 4p, 8p, ... -cycles).
e.g. a period 3 window is   3.8285 < a < 3.8494  (3.857)