Question

I want to randomly generate points. Well at least there should be a limitation on the y-axis. Later I connect the points to a line which should proceed in a simple animation. You can imagine this as a random walk of a drunken person, going uphill and downhill.

This sounds very simple. I searched around the web and found that this could be accomplished using the markov chain. I think this idea is really interesting.

You can create the first state of your scene by yourself and pass this state as input to the markov chain algorithm. The algorithm randomly changes this state and creates a walk.

However I cannot find any example of that algorithm and no source code. I just found an applet that demonstrates the markov chain algorithm: http://www.probability.ca/jeff/java/unif.html

Please suggest some code. Any other ideas how to accomplish this are appreciated too.

I painted an example

So I want the line to proceed in a similar way. There are valleys, slopes … they are random but the randomness still apply to the initial state of the line. This is why I found makrov chain so interesting here: http://www.suite101.com/content/implementing-markov-chains-a24146

Answer 1

Here’s some code in Lua:

absstepmax = 25
ymin = -100
ymax = 100
x = 0
y = 5
for i = 1, 20 do
    y = y + (math.random(2*absstepmax) - absstepmax - 1)
    y = math.max(ymin, math.min(ymax, y))
    x = x + 5
    print (x,y)
end

absstepmax limits the size of a y step per iteration

ymin and ymax limit the extent of y

There is no bias in the example, i.e., y can change symmetrically up or down. If you want your “drunk” tending more “downhill” you can change the offset after the call to random from absstepmax - 1 to absstepmax - 5 or whatever bias you like.

In this example, the x step is fixed. You may make this random as well using the same mechanisms.

Here are some sample runs:

> absstepmax = 25
> ymin = -100
> ymax = 100
> x = 0
> y = 5
> for i = 1, 20 do
>>     y = y + (math.random(2*absstepmax) - absstepmax - 1)
>>     y = math.max(ymin, math.min(ymax, y))
>>     x = x + 5
>>     print (x,y)
>> end
5   4
10  22
15  37
20  39
25  50
30  40
35  21
40  22
45  12
50  16
55  16
60  12
65  -1
70  -8
75  -14
80  -17
85  -19
90  -25
95  -37
100 -59
> absstepmax = 25
> ymin = -100
> ymax = 100
> x = 0
> y = 5
> for i = 1, 20 do
>>     y = y + (math.random(2*absstepmax) - absstepmax - 1)
>>     y = math.max(ymin, math.min(ymax, y))
>>     x = x + 5
>>     print (x,y)
>> end
5   -2
10  -15
15  -7
20  1
25  1
30  12
35  23
40  45
45  43
50  65
55  56
60  54
65  54
70  62
75  57
80  62
85  86
90  68
95  76
100 68
> 

Painted result added from OP: