Trieste Lectures 2015
From Werner KRAUTH
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!Lecture 2: Programs | !Lecture 2: Programs | ||
+ | This is markov-disks-box.py | ||
+ | import random | ||
+ | |||
+ | L = [[0.25, 0.25], [0.75, 0.25], [0.25, 0.75], [0.75, 0.75]] | ||
+ | sigma = 0.15 | ||
+ | sigma_sq = sigma ** 2 | ||
+ | delta = 0.1 | ||
+ | n_steps = 1000 | ||
+ | for steps in range(n_steps): | ||
+ | a = random.choice(L) | ||
+ | b = [a[0] + random.uniform(-delta, delta), a[1] + random.uniform(-delta, delta)] | ||
+ | min_dist = min((b[0] - c[0]) ** 2 + (b[1] - c[1]) ** 2 for c in L if c != a) | ||
+ | box_cond = min(b[0], b[1]) < sigma or max(b[0], b[1]) > 1.0 - sigma | ||
+ | if not (box_cond or min_dist < 4.0 * sigma ** 2): | ||
+ | a[:] = b | ||
+ | print L | ||
This is lift-two-disks.py | This is lift-two-disks.py |
Revision as of 11:51, 15 September 2015
!Lecture 1: Programs
!Lecture 2: Programs This is markov-disks-box.py
import random L = [[0.25, 0.25], [0.75, 0.25], [0.25, 0.75], [0.75, 0.75]] sigma = 0.15 sigma_sq = sigma ** 2 delta = 0.1 n_steps = 1000 for steps in range(n_steps): a = random.choice(L) b = [a[0] + random.uniform(-delta, delta), a[1] + random.uniform(-delta, delta)] min_dist = min((b[0] - c[0]) ** 2 + (b[1] - c[1]) ** 2 for c in L if c != a) box_cond = min(b[0], b[1]) < sigma or max(b[0], b[1]) > 1.0 - sigma if not (box_cond or min_dist < 4.0 * sigma ** 2): a[:] = b print L
This is lift-two-disks.py
import math, random def dist(x, y): d_x = abs(x[0] - y[0]) % 1.0 d_x = min(d_x, 1.0 - d_x) d_y = abs(x[1] - y[1]) % 1.0 d_y = min(d_y, 1.0 - d_y) return d_x**2 + d_y**2 L = [[0.25, 0.25], [0.75, 0.75]] sigma = 0.18 for steps in range(10000): delta = random.uniform(0.0, 0.04) lift = random.choice([0, 1]) a = L[lift] dirc = random.choice([0, 1]) for inner_steps in range(100): b = a[:] b[dirc] += delta distance = dist(b, L[int( not lift)]) if distance > 4.0 * sigma ** 2: a[:] = [b[0] % 1.0, b[1] % 1.0] else: lift = int(not lift) a = L[lift]
This is event-chain.py
import random, math def event(a, b, dirc, sigma): d_perp = abs(b[not dirc] - a[not dirc]) % 1.0 d_perp = min(d_perp, 1.0 - d_perp) if d_perp > 2.0 * sigma: return float("inf") else: d_para = math.sqrt(4.0 * sigma ** 2 - d_perp ** 2) return (b[dirc] - a[dirc] - d_para + 1.0) % 1.0 L = [[0.25, 0.25], [0.25, 0.75], [0.75, 0.25], [0.75, 0.75]] ltilde = 0.819284; sigma = 0.15 for iter in xrange(20000): dirc = random.randint(0, 1) print iter, dirc, L distance_to_go = ltilde next_a = random.choice(L) while distance_to_go > 0.0: a = next_a event_min = distance_to_go for b in [x for x in L if x != a]: event_b = event(a, b, dirc, sigma) if event_b < event_min: next_a = b event_min = event_b a[dirc] = (a[dirc] + event_min) % 1.0 distance_to_go -= event_min