# Questions tagged [random]

Questions about random number generation and the properties of numbers so generated.

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8answers
6k views

### How to generate random points in a region?

The Mathematica 10 documentation was updated for FindInstance adding support for regions. In my use case, I'm trying to sample points in a set of disks: ...
7answers
6k views

### Efficient way to generate random points with a predefined lower bound on their pairwise Euclidean distance

Using Mathematica what is an efficient way to generate a list of $n$ random two dimensional points $\{x_i,y_i\}$ where $i=1,...,n$ so that no two points $p_1$ and $p_2$ in the list has an Euclidean ...
3answers
2k views

### Uniformly distributed n-dimensional probability vectors over a simplex

What's the right way to generate a random probability vector $p={p_1,\ldots,p_n} \in {(0,1)}^n$ where $\sum_i p_i=1$, uniformly distributed over the $(n-1)$-dimensional simplex? What I have is ...
2answers
4k views

### RandomVariate from 2-dimensional probability distribution

A probability distribution can be created in Mathematica (I am using 8.0.1) with e.g. ...
6answers
4k views

### 2D random walk within a bounded area

I want to simulate a random walk in two dimensions within a bounded area, such as a square or a circle. I am thinking of using an If statement to define a boundary. ...
5answers
1k views

### obtaining random element of a set given by multiple inequalities

I try to obtain random elements from a set given by multiple inequalities. This is of general interest to me, but let me present one example here: I have multiple inequalities specifying half spaces ...
5answers
5k views

### Efficiently generating n-D Gaussian random fields

I am interested in an efficient code to generate an $n$-D Gaussian random field (sometimes called processes in other fields of research), which has applications in cosmology. Attempt I wrote the ...
4answers
1k views

### Which Distributions can be Compiled using RandomVariate

Recently, Oleksandr kindly showed a list of Mathematica commands that can be compiled. RandomVariate was part of that list. However, whether this can be compiled depends upon the distribution that is ...
6answers
4k views

### Vectors with a certain magnitude in Mathematica

For a user-specified magnitude, is there a way to have Mathematica produce any 3D vector with that magnitude?
3answers
11k views

### How to generate a RandomVariate of a custom distribution?

I'm trying to generate a pseudorandom variate out of a custom distribution. Suppose I want define a custom distribution, and for the sake of simplicity I define a Poisson distribution (the ...
9answers
16k views

### How to create animated snowfall?

Well, the title is self-explanatory. What sorts of snowfall can we generate using Mathematica? There are two options I suggest to consider: 1) Continuous GIF animations with smallest possible number ...
4answers
3k views

### Can Mathematica's random number generation be improved?

Performance on Random Number generation is intolerable. Whenever you need many deviates from the same distribution but with different parameters it takes forever. Here is a thread on Poisson deviates ...
2answers
2k views

### Monte Carlo integration with random numbers generated from a Gaussian distribution

I want to do numerical integration of some functions using the Monte Carlo method. The default setting for the Monte Carlo method is to use a uniform distribution as far as I know. How can I change ...
5answers
5k views

### Distribution of random points in 3D space to simulate the Crab Nebula

I'm generating some 3D models of planetary nebulae and supernova remnants for Celestia, a free OpenGL astronomy software. Currently, I know how to do it with random points inside a spherical shell. ...
11answers
6k views

### Random numbers that sum up to specific value

I would like to generate a list with random numbers, which add up to a specific value. While[Total[x] == 28, x = RandomInteger[{0, 28}, 5];Print[x]] The random ...
3answers
10k views

### How to generate random directed acyclic graphs?

How to programmatically build random directed acyclic graphs (DAG)? I know about the AcyclicGraphQ predicate and the ...
4answers
6k views

### Randomly packing spheres of fixed radius within a cube

How can I have Mathematica randomly place spheres in a cube so they won't overlap? The cube is $20 \times 20 \times 20$, and the spheres have a radius of $0.7$.
1answer
2k views

### Randomly selecting elements without repetition

I assigned energy values to each element in the array as per the program of Verbeia. The program looks like this ...
7answers
28k views

### How to generate a random snowflake

'Tis the season... And it's about time I posed my first question on Mathematica Stack Exchange. So, here's an holiday quest for you Graphics (and P-Chem?) gurus. What is your best code for generating ...
1answer
630 views

### Simulating Theatre puzzle

I have been trying to simulate the process of the theatre puzzle from the Joy of X (Strogatz). The puzzle, and some relevant material are here. My simplistic coding for this process follows: ...
6answers
3k views

### Generate two random numbers with constraints

I want to generate two random numbers, $p$ and $q$, between $0.5$ and $1$. They are connected by the constraint $1/(2q) > p$. How do I generate $p$ and $q$?
2answers
393 views

### generating randomly oriented non-intersecting cylinders

I could not find anything relevant with "googling" (only this) I can create a set of randomly oriented cylinders (code found here) ...
3answers
4k views

### Quality of random numbers

Mathematica has several ways of generating random numbers: Congruential, ExtendedCA, Legacy, MersenneTwister, MKL, ParallelGenerator, ParallelMersenneTwister, Rule30CA. For ...
1answer
1k views

### Speed up adding Poisson noise to an image

I'm simulating some images corrupted with Poisson noise, but I'm encountering a few problems with performance. According to the documentation on ImageEffect, one ...
5answers
1k views

### How can I generate and randomly assign color to annular sectors?

How can I generate such an image and fill every annular sector with a random colour?
4answers
2k views

### Random real numbers that sum up to specific value [duplicate]

In here, it works with "Integer". What if I want 5 positive real numbers that sum to 1? RandomChoice[IntegerPartitions[100, {5}]]/100. That will work. But only ...
3answers
1k views

### Random non-overlapping disks in a square

I've found a nice code snippet by @belisarius from this question, that I'll reproduce here for reference: ...
1answer
3k views

### Finding the likeliest path in a Markov process

With Mathematica 9, we have the addition of various processes, among which the discrete Markov process. Given a transition probability matrix m, such a process is ...
3answers
6k views

### Create triangular mesh from random list of points

I have a list of points. I would like to take these points and create a mesh of triangles from them, making sure triangles don't overlap. So here's a list of points: ...
4answers
2k views

### 3D Random Walk with Periodic Boundary Conditions

I am working on a 3D random walk with periodic boundary conditions and have written a program that will do this for me, but it is extremely slow. Does anyone have any suggestions on how I could speed ...
2answers
911 views

### What will happen, if I don't specify random seed by SeedRandom function?

Suppose I want to run several times of the same code containing RandomReal function, but I don't initialise the random seed. What will happen? I tried, but each ...
8answers
478 views

### Is it possible to use RandomChoice to choose without other choices being evaluated?

I'm trying to do this: i1 = 1; i2 = 1; RandomChoice[{ (i1 = i1 + 1), (i1 = i1 - 1), (i2 = i1 + 1), (i2 = i2 - 1)}] In order to chose randomly which ...
3answers
676 views

### Creating random configurations of spherocylinders or cylinders

About the setting: We have a 3D simulation box with side $l$ and our catesian coordinate system is set with its origin at the centre of the box. We have a number $N$ of spherocylinders of aspect ...
4answers
997 views

### Why is Poisson Random Deviate Generation so slow?

I am generating Poisson deviates for some numerical work. Mathematica 9.0.1 is very slow in generating these random numbers, as can be seen below. ...
3answers
656 views

### Turning a set of random walk data 45 degrees

I have a set of data that is just a "random" (generated by me, not by computer) sequence of length 2000 of 1's and (-1)'s. I used it to plot a 1-D random walk where +1 is step up, (-1) is step down, ...
2answers
132 views

### Sum considers RandomInteger[] as a constant

Perhaps this is expected behavior, but I was kind of surprised by the following: ...
2answers
867 views

### How-to cast a set of random points on the surface of a cuboid?

I have been able to implement point picking for cylinders and spheres. However, I struggle to implement a solution for a cuboid. Please see code for point generation on cylinders and spheres below: ...
1answer
478 views

### Are there rules of thumb for knowing when RandomVariate is more efficient than RandomReal?

Please consider the following: From a fresh Mathematica kernel, RandomVariate is more efficient for NormalDistribution but <...
1answer
152 views

### Huge overhead in RandomPoint[ImplicitRegion]

Commenting answers of this question @JasonB noticed the big overhead of RandomPoint ...
1answer
344 views

### Sample of the random times at which the random walk crosses the boundary

I defined a security boundary for a random walk: ...
5answers
2k views

### Assigning a particular value to array elements

I have an array of 10000 elements. I want to randomly assign energy to these 10000 elements using Gaussian or Exponential distribution, such that each time a particular element is selected its energy ...
1answer
170 views

### How can one generate an open-ended sequence of low-discrepancy points in 3D?

I'd like a low-discrepancy sequence of points over a 3D-hypercube $[-1,1]^3$, but don't want to have to commit to a fixed number $n$ of points beforehand, that is just see how the numerical ...
1answer
190 views

### Generate $n$ randomly oriented non-intersecting cylinders with fixed radius and length

This post is in reference to the previous question here. How could I adapt the solution given to have the following constraints: fixed radius, fixed length, number of cylinders, and within a ...
4answers
5k views

### Finding the volume of a sphere using the Monte Carlo algorithm

I used the following code to find the volume of the sphere $x^2+y^2+z^2 \leq 1$ in the first octant: ...
3answers
3k views

### Generate a Random Polygon

Does some package exist with a function that takes a parameter $n$ and generates a random 2D $n$-sided simple polygon (convex or non-convex), possibly within a certain bounding box? It does not ...
2answers
1k views

### Efficient Generation of Random Variates from a Copula Distribution

I have a 7-asset portfolio for which I want to simulate daily log-deltas using a Student T copula. The marginal distributions are all either Stable or TsallisQGaussian. Using NMaximize, I have ...
5answers
2k views

### Picking random items out of a list only once

I'm trying to create a function that randomly returns a value from a list but remembers the values that have been given before. At the end when the list is empty it should return an empty list. ...
2answers
783 views

### Fast Simulations with Compile

this post relates to another post that I didn't follow up propely. If I wanted to simulate a system of stochastic proesses like the following, and loop over this run many many times would writing the ...
2answers
6k views

### What is the best distribution for my histogram?

I defined a security bound for a random walk (cube with 15 length) and I have this code to obtain a sample of the random times at which the random walk crosses the boundary for the first time: ...
3answers
1k views

### 1D Random Walk variant

I am making a notebook that is a variation to the traditional 1d random walk problem. The normal 1D random walk can be simulated easily by ...