f(x)=

(a_1,0)

y=f(f(x))

y=f(f(f(x)))(when a=1+2√2)

y=f\circ f\circ f(x)

y=f\circ f(x)

nを1つ増加

nを1つ減少

a = 3.34 (slider from 0.5 to 4, step 0.01)
f(x) = ((a * x) * (1 - x))
A = Point(xAxis)
c: x(A)
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f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(c))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
N = Length(values)
InputBox1 = Textfield(f)
id: y = x
ptonf = Sequence((Element[values, k], Element[values, k + 1]), k, 1, N - 1)
ptonid = Sequence((Element[values, k], Element[values, k]), k, 2, N)
allpts = Append(A, Flatten[Zip[{a, b}, a, ptonf, b, ptonid]])
n = 55 (slider from 1 to 100, step 1)
pts = Take(allpts, 1, n)
g(x) = f(f(x))
gShow = true
h(x) = f(f(f(x)))
hShow = false
zigzagline = PolyLine(Take[pts, 1, n - 1])
u = If(n > 1, Vector[Element[pts, n - 1], Element[pts, n]])

Tool: mkptsonarc
mkptsonarc[ <Point>, <Circle>, <Point>, <Number>, <Number> ]
Input: A, c, B, delta, M
Output: ptsonarc

D = Center(c)
Na: ceil(c / delta)
Narc: (1 / 2 * (Na - M - abs(Na - M))) + M
ptsonarc = If(Defined[Intersect[c, ((A - D) * ℯ^((ί * Angle[A, D, B] / 2))) + D]], Sequence[((A - D) * ℯ^(((ί * k) * Angle[A, D, B] / Narc))) + D, k, 0, Narc - 1], Sequence[((A - D) * ℯ^((((-ί) * k) * Angle[B, D, A] / Narc))) + D, k, 0, Narc - 1])

Tool: mkptsonseg
mkptsonseg[ <Point>, <Point>, <Number>, <Number> ]
Input: A, B, delta, M
Output: ptsonseg

f = Segment(A, B)
Ns: ceil(f / delta)
N: (1 / 2 * (Ns - M - abs(Ns - M))) + M
ptsonseg = Sequence(((1 - k / N) * ToComplex[A]) + (k / N * ToComplex[B]), k, 0, N - 1)