connect

r = 2 (slider from 0 to 4, step 0.005)
f(x) = ((r * x) * (1 - x))
seed = 0.25 (slider from 0 to 1, step 0.01)
A1 = 0
A2 = 1
A3 = 2
A4 = 3
A5 = 4
A6 = 5
A7 = 6
A8 = 7
A9 = 8
A10 = 9
A11 = 10
A12 = 11
A13 = 12
A14 = 13
A15 = 14
A16 = 15
A17 = 16
A18 = 17
A19 = 18
A20 = 19
A21 = 20
A22 = 21
B1: seed
B2: f(B1)
A23: (2 * A22) - A21
A24: (2 * A23) - A22
A25: (2 * A24) - A23
A26: (2 * A25) - A24
A27: (2 * A26) - A25
A28: (2 * A27) - A26
A29: (2 * A28) - A27
A30: (2 * A29) - A28
A31: (2 * A30) - A29
A32: (2 * A31) - A30
A33: (2 * A32) - A31
A34: (2 * A33) - A32
A35: (2 * A34) - A33
A36: (2 * A35) - A34
A37: (2 * A36) - A35
A38: (2 * A37) - A36
A39: (2 * A38) - A37
A40: (2 * A39) - A38
A41: (2 * A40) - A39
A42: (2 * A41) - A40
A43: (2 * A42) - A41
A44: (2 * A43) - A42
A45: (2 * A44) - A43
A46: (2 * A45) - A44
B3: f(B2)
B4: f(B3)
B5: f(B4)
B6: f(B5)
B7: f(B6)
B8: f(B7)
B9: f(B8)
B10: f(B9)
B11: f(B10)
B12: f(B11)
B13: f(B12)
B14: f(B13)
B15: f(B14)
B16: f(B15)
B17: f(B16)
B18: f(B17)
B19: f(B18)
B20: f(B19)
B21: f(B20)
B22: f(B21)
B23: f(B22)
B24: f(B23)
B25: f(B24)
B26: f(B25)
B27: f(B26)
B28: f(B27)
B29: f(B28)
B30: f(B29)
B31: f(B30)
B32: f(B31)
B33: f(B32)
B34: f(B33)
B35: f(B34)
B36: f(B35)
B37: f(B36)
B38: f(B37)
B39: f(B38)
B40: f(B39)
B41: f(B40)
B42: f(B41)
B43: f(B42)
B44: f(B43)
B45: f(B44)
B46: f(B45)
o = false
O_2 = Intersect(f, xAxis, 2)
a_1 = OrthogonalLine(O_2, xAxis)
Q_2: (0, 1)
top = OrthogonalLine(Q_2, yAxis)
C1: B1
C2: B2
C3: B3
C4: B4
C5: B5
C6: B6
C7: B7
C8: B8
C9: B9
C10: B10
C11: B11
C12: B12
C13: B13
C14: B14
C15: B15
C16: B16
C17: B17
C18: B18
C19: B19
C20: B20
C21: B21
C22: B22
C23: B23
C24: B24
C25: B25
C26: B26
C27: B27
C28: B28
C29: B29
C30: B30
C31: B31
C32: B32
C33: B33
C34: B34
C35: B35
C36: B36
C37: B37
C38: B38
C39: B39
C40: B40
C41: B41
C42: B42
C43: B43
C44: B44
C45: B45
C46: B46
D1: C2
D2: C3
D3: C4
D4: C5
D5: C6
D6: C7
D7: C8
D8: C9
D9: C10
D10: C11
D11: C12
D12: C13
D13: C14
D14: C15
D15: C16
D16: C17
D17: C18
D18: C19
D19: C20
D20: C21
D21: C22
D22: C23
D23: C24
D24: C25
D25: C26
D26: C27
D27: C28
D28: C29
D29: C30
D30: C31
D31: C32
D32: C33
D33: C34
D34: C35
D35: C36
D36: C37
D37: C38
D38: C39
D39: C40
D40: C41
D41: C42
D42: C43
D43: C44
D44: C45
D45: C46
R_2: (B1, C1)
S_2: (B2, C2)
T_2: (B3, C3)
U_2: (B4, C4)
V_2: (B5, C5)
W_2: (B6, C6)
Z_2: (B7, C7)
A_3: (B8, C8)
B_3: (B9, C9)
C_3: (B10, C10)
D_3: (B11, C11)
E_3: (B12, C12)
F_3: (B13, C13)
G_3: (B14, C14)
H_3: (B15, C15)
I_3: (B16, C16)
J_3: (B17, C17)
K_3: (B18, C18)
L_3: (B19, C19)
M_3: (B20, C20)
N_3: (B21, C21)
O_3: (B22, C22)
P_3: (B23, C23)
Q_3: (B24, C24)
R_3: (B25, C25)
S_3: (B26, C26)
T_3: (B27, C27)
U_3: (B28, C28)
V_3: (B29, C29)
W_3: (B30, C30)
Z_3: (B31, C31)
A_4: (B32, C32)
B_4: (B33, C33)
C_4: (B34, C34)
D_4: (B35, C35)
E_4: (B36, C36)
F_4: (B37, C37)
G_4: (B38, C38)
H_4: (B39, C39)
I_4: (B40, C40)
J_4: (B41, C41)
K_4: (B42, C42)
L_4: (B43, C43)
M_4: (B44, C44)
N_4: (B45, C45)
O_4: (B46, C46)
twins: {R_2, S_2, T_2, U_2, V_2, W_2, Z_2, A_3, B_3, C_3, D_3, E_3, F_3, G_3, H_3, I_3, J_3, K_3, L_3, M_3, N_3, O_3, P_3, Q_3, R_3, S_3, T_3, U_3, V_3, W_3, Z_3, A_4, B_4, C_4, D_4, E_4, F_4, G_4, H_4, I_4, J_4, K_4, L_4, M_4, N_4, O_4}
P_4: (C1, D1)
Q_4: (C2, D2)
R_4: (C3, D3)
S_4: (C4, D4)
T_4: (C5, D5)
U_4: (C6, D6)
V_4: (C7, D7)
W_4: (C8, D8)
Z_4: (C9, D9)
A_5: (C10, D10)
B_5: (C11, D11)
C_5: (C12, D12)
D_5: (C13, D13)
E_5: (C14, D14)
F_5: (C15, D15)
G_5: (C16, D16)
H_5: (C17, D17)
I_5: (C18, D18)
J_5: (C19, D19)
K_5: (C20, D20)
L_5: (C21, D21)
M_5: (C22, D22)
N_5: (C23, D23)
O_5: (C24, D24)
P_5: (C25, D25)
Q_5: (C26, D26)
R_5: (C27, D27)
S_5: (C28, D28)
T_5: (C29, D29)
U_5: (C30, D30)
V_5: (C31, D31)
W_5: (C32, D32)
Z_5: (C33, D33)
A_6: (C34, D34)
B_6: (C35, D35)
C_6: (C36, D36)
D_6: (C37, D37)
E_6: (C38, D38)
F_6: (C39, D39)
G_6: (C40, D40)
H_6: (C41, D41)
I_6: (C42, D42)
J_6: (C43, D43)
K_6: (C44, D44)
L_6: (C45, D45)
M_6: (C1, D1)
N_6: (C2, D2)
O_6: (C3, D3)
P_6: (C4, D4)
Q_6: (C5, D5)
R_6: (C6, D6)
S_6: (C7, D7)
T_6: (C8, D8)
U_6: (C9, D9)
V_6: (C10, D10)
W_6: (C11, D11)
Z_6: (C12, D12)
A_7: (C13, D13)
B_7: (C14, D14)
C_7: (C15, D15)
D_7: (C16, D16)
E_7: (C17, D17)
F_7: (C18, D18)
G_7: (C19, D19)
H_7: (C20, D20)
I_7: (C21, D21)
J_7: (C22, D22)
K_7: (C23, D23)
L_7: (C24, D24)
M_7: (C25, D25)
N_7: (C26, D26)
O_7: (C27, D27)
P_7: (C28, D28)
Q_7: (C29, D29)
R_7: (C30, D30)
S_7: (C31, D31)
T_7: (C32, D32)
U_7: (C33, D33)
V_7: (C34, D34)
W_7: (C35, D35)
Z_7: (C36, D36)
A_8: (C37, D37)
B_8: (C38, D38)
C_8: (C39, D39)
D_8: (C40, D40)
E_8: (C41, D41)
F_8: (C42, D42)
G_8: (C43, D43)
H_8: (C44, D44)
I_8: (C45, D45)
images: {M_6, N_6, O_6, P_6, Q_6, R_6, S_6, T_6, U_6, V_6, W_6, Z_6, A_7, B_7, C_7, D_7, E_7, F_7, G_7, H_7, I_7, J_7, K_7, L_7, M_7, N_7, O_7, P_7, Q_7, R_7, S_7, T_7, U_7, V_7, W_7, Z_7, A_8, B_8, C_8, D_8, E_8, F_8, G_8, H_8, I_8}
n = 0 (slider from 0 to 45, step 1)
A: (A1, B1)
B: (A2, B2)
C: (A3, B3)
D: (A4, B4)
E: (A5, B5)
F: (A6, B6)
G: (A7, B7)
H: (A8, B8)
I: (A9, B9)
J: (A10, B10)
K: (A11, B11)
L: (A12, B12)
M: (A13, B13)
N: (A14, B14)
O: (A15, B15)
P: (A16, B16)
Q: (A17, B17)
R: (A18, B18)
S: (A19, B19)
T: (A20, B20)
U: (A21, B21)
V: (A22, B22)
W: (A23, B23)
Z: (A24, B24)
A_1: (A25, B25)
B_1: (A26, B26)
C_1: (A27, B27)
D_1: (A28, B28)
E_1: (A29, B29)
F_1: (A30, B30)
G_1: (A31, B31)
H_1: (A32, B32)
I_1: (A33, B33)
J_1: (A34, B34)
K_1: (A35, B35)
L_1: (A36, B36)
M_1: (A37, B37)
N_1: (A38, B38)
O_1: (A39, B39)
P_1: (A40, B40)
Q_1: (A41, B41)
R_1: (A42, B42)
S_1: (A43, B43)
T_1: (A44, B44)
U_1: (A45, B45)
V_1: (A46, B46)
orbit: {A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, U_1, V_1}
showOrbit = Sequence(Element[orbit, i], i, 0, n)
steps = Sequence(PolyLine[Element[twins, i], Element[images, i], Element[twins, i + 1]], i, 0, n)
showTwins = Sequence(Element[twins, i], i, 0, n)
ShowImages = Sequence(Element[images, i], i, 0, n)
Z_1 = (0.6644295302013423, 0.6644295302013423)
int: x(Z_1)
B_2 = Intersect(f, b, (-9.071900410041636E-30, -1.8143800820083272E-29))
C_2 = Intersect(((-(x(b) / y(b))) * x) - z(b) / y(b), f, (0, 0))
right: x = 1
text1: "f(x) = " + (LaTeX[f]) + ""
a = PolyLine(showOrbit)