Erratic Systematic Wormhole Mathematics

Computer Science Level 3

Chaos has emerged in a 1×1 field; The fabric of space will never be healed.

The limits of light have been replaced: All matter is teleported to a random place!

How far is the average point displaced?

This rule of space should not be disregarded: You might teleport to exactly where you started.

Hint: Don't set your bar low. Use Monte-Carlo .


The answer is 0.52.

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Brock Brown by Brock Brown , 25, USA

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5 solutions

MATLAB Code: 

        [X,Y]=meshgrid(0:.01:1,0:.01:1);
         for i=1:10000
       P = randperm(prod(size(X)));
        X1 = X(P);Y1=Y(P);
        D = ((X1-X(:)).^2+(Y1-Y(:)).^2).^.5;
         S(i)=mean(D);
         end
         result = mean(S);
7 Helpful 2 Interesting 0 Brilliant 0 Confused
Brock Brown
Feb 6, 2015

Python: 

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from random import random as r
from math import sqrt
def distance(a,b,c,d):
    return sqrt(abs((a-c)**2+(b-d)**2))
total = 0.0
trials = 10000000
for i in xrange(trials):
    total += distance(r(),r(),r(),r())
print "Answer:", total / trials

9 Helpful 1 Interesting 0 Brilliant 2 Confused

Sage Code: 

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def monte_carlo():
    x1, y1,x2, y2 = random(), random(), random(), random()
    return sqrt((x1-x2)^2 + (y1-y2)^2)
l1 = map(lambda n: monte_carlo(),xrange(1000000))
print sum(l1)/len(l1)

3 Helpful 1 Interesting 1 Brilliant 0 Confused

Sage is a cool language, I'm surprised more people don't use it.

Brock Brown - 6 years, 4 months ago
Piotr Idzik
Feb 13, 2020

R code: 

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distanceL2 <- function(vec_a, vec_b)
{
  return(sqrt(sum((vec_a-vec_b)^2)))
}

getRandomDist <- function()
{
  return(distanceL2(runif(2, 0, 1), runif(2, 0, 1)))
}

distData = replicate(10000000, getRandomDist())
print(mean(distData))

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Wang Xingyu
Sep 17, 2020 
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import numpy as np 
a = np.random.rand(2,10000000)
b = np.random.rand(2,10000000)
d = np.sqrt(sum((a - b)**2))
print(np.average(d))    # 0.5214153207282254

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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