1. samm

2. samm

3. samm

(0,0)

(0,1)

(1,1)

(0,1)

Lõikude arv

Lõigu pikkus

Kogu pikkus

Samm

Hilberti kõvera pikkus

Tähised: \
k - samm \
N_{i} - lõikude \; arv \; i-ndal \; sammul \
L_{i} - lõigu \; pikkus\; i-ndal \; sammul \
D_{i} - kogu pikkus\; i-ndal \; sammul

Esimesel \; sammul: \
N_{1}=3 \
L_{1}=0.5 \
D_{1}=N_{1}·L_{1}=3·0.5=1.5

Vaatame \; ühikruudu \; sisse \; joonistatud \; Hilberti \; kõverat.

Teisel \; sammul: \
N_{2}=N_{1}·4+3=3·4+3=15 \
L_{2}=L_{1}÷2=0.5÷2=0.25 \
D_{2}=N_{2}·L_{2}=15·0.25=3.75

k-ndal \; sammul: \
N_{k}=N_{k-1}·4+3 = 2^{2k}-1 \
L_{k}=L_{k-1}÷2 =2^{-k}\
D_{k}=N_{k}·L_{k}= \frac{2^{2k} -1}{2^k}=2^{k}-2^{-k}

A = Point(yAxis)
B = (8, 8)
C = Point(xAxis)
D = (4, 4)
E = (2, 2)
F = (2, 6)
G = (6, 6)
H = (6, 2)
h = PolyLine(E, F, G, H)
I = (1, 1)
J = (3, 1)
K = (3, 3)
L = (1, 3)
M = (1, 5)
N = (1, 7)
O = (3, 7)
P = (3, 5)
Q = (5, 5)
R = (5, 7)
S = (7, 7)
T = (7, 5)
U = (7, 3)
V = (5, 3)
W = (5, 1)
Z = (7, 1)
i = PolyLine(I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, Z)
A_1 = (0.5, 0.5)
B_1 = (0.5, 1.5)
C_1 = (1.5, 1.5)
D_1 = (1.5, 0.5)
E_1 = (2.5, 0.5)
F_1 = (3.5, 0.5)
G_1 = (3.5, 1.5)
H_1 = (2.5, 1.5)
I_1 = (2.5, 2.5)
J_1 = (3.5, 2.5)
K_1 = (3.5, 3.5)
L_1 = (2.5, 3.5)
M_1 = (1.5, 3.5)
N_1 = (1.5, 2.5)
O_1 = (0.5, 2.5)
P_1 = (0.5, 3.5)
Q_1 = (0.5, 4.5)
R_1 = (1.5, 4.5)
S_1 = (1.5, 5.5)
T_1 = (0.5, 5.5)
U_1 = (0.5, 6.5)
V_1 = (0.5, 7.5)
W_1 = (1.5, 7.5)
Z_1 = (1.5, 6.5)
A_2 = (2.5, 6.5)
B_2 = (2.5, 7.5)
C_2 = (3.5, 7.5)
D_2 = (3.5, 6.5)
E_2 = (3.5, 5.5)
F_2 = (2.5, 5.5)
G_2 = (2.5, 4.5)
H_2 = (3.5, 4.5)
I_2 = (4.5, 4.5)
J_2 = (5.5, 4.5)
K_2 = (5.5, 5.5)
L_2 = (4.5, 5.5)
M_2 = (4.5, 6.5)
N_2 = (4.5, 7.5)
O_2 = (5.5, 7.5)
P_2 = (5.5, 6.5)
Q_2 = (6.5, 6.5)
R_2 = (6.5, 7.5)
S_2 = (7.5, 7.5)
T_2 = (7.5, 6.5)
U_2 = (7.5, 5.5)
V_2 = (6.5, 5.5)
W_2 = (6.5, 4.5)
Z_2 = (7.5, 4.5)
A_3 = (7.5, 3.5)
B_3 = (7.5, 2.5)
C_3 = (6.5, 2.5)
D_3 = (6.5, 3.5)
E_3 = (5.5, 3.5)
F_3 = (4.5, 3.5)
G_3 = (4.5, 2.5)
H_3 = (5.5, 2.5)
I_3 = (5.5, 1.5)
J_3 = (4.5, 1.5)
K_3 = (4.5, 0.5)
L_3 = (5.5, 0.5)
M_3 = (6.5, 0.5)
N_3 = (6.5, 1.5)
O_3 = (7.5, 1.5)
P_3 = (7.5, 0.5)
j = PolyLine(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, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, 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 = Intersect(xAxis, yAxis)
R_3 = (0, 8)
S_3 = (8, 8)
T_3 = (8, 0)
q1, q_3, r_3, s_3, t_3 = Polygon(Q_3, R_3, S_3, T_3)
A5: 1
B5: 3
C5: 0.500000000000001
A6: 2
B6: (B5 * 4) + 3
C6: C5 / 2
A7: 3
B7: (B6 * 4) + 3
C7: C6 / 2
A8: 4
B8: (B7 * 4) + 3
C8: C7 / 2
A9: 5
B9: (B8 * 4) + 3
C9: C8 / 2
A10: 6
B10: (B9 * 4) + 3
C10: C9 / 2
A11: 7
B11: (B10 * 4) + 3
C11: C10 / 2
A12: 8
B12: (B11 * 4) + 3
C12: C11 / 2
A13: 9
B13: (B12 * 4) + 3
C13: C12 / 2
A14: 10
B14: (B13 * 4) + 3
C14: C13 / 2
A15: 11
B15: (B14 * 4) + 3
C15: C14 / 2
A16: 12
B16: (B15 * 4) + 3
C16: C15 / 2
A17: 13
B17: (B16 * 4) + 3
C17: C16 / 2
A18: 14
B18: (B17 * 4) + 3
C18: C17 / 2
A19: 15
B19: (B18 * 4) + 3
C19: C18 / 2
A20: 16
B20: (B19 * 4) + 3
C20: C19 / 2
A21: 17
B21: (B20 * 4) + 3
C21: C20 / 2
A22: 18
B22: (B21 * 4) + 3
C22: C21 / 2
A23: 19
B23: (B22 * 4) + 3
C23: C22 / 2
A24: 20
B24: (B23 * 4) + 3
C24: C23 / 2
D5: (B5 * C5)
D6: (B6 * C6)
D7: (B7 * C7)
D8: (B8 * C8)
D9: (B9 * C9)
D10: (B10 * C10)
D11: (B11 * C11)
D12: (B12 * C12)
D13: (B13 * C13)
D14: (B14 * C14)
D15: (B15 * C15)
D16: (B16 * C16)
D17: (B17 * C17)
D18: (B18 * C18)
D19: (B19 * C19)
D20: (B20 * C20)
D21: (B21 * C21)
D22: (B22 * C22)
D23: (B23 * C23)
D24: (B24 * C24)