Real Number Walks versus Algorithmic Random Walks

type of walk

1D walk

2D walk

3D walk

irrational number

π



ϕ



2

log(2)

p

number of random walks

0

1

2

3

4

max number of steps

100

500

1000

2000

step

75

seed

1

1D walks

1D randomize

2D walks

2D randomize

base

3

4

5

6

7

8

9

10

12

16

3D walks

3D randomize

reveal legends

This Demonstration compares an irrational number walk (based on its digital expansion) with algorithmic random walks. The irrational number walks are mathematical constants

π

,

e

,

ϕ

(the golden ratio),

γ

(Euler–Mascheroni constant),

2

, log(2) and

p

, where

p

is a prime; they seem to be indistinguishable from algorithmic random walks.

Walks based on the digits of Liouville's constant and the like, which omit some digits entirely, clearly cannot be considered random at all.