t, let's talk about randomness. Randomness is a problem in computing because digital computers are deterministic. If you give them the exact same instructions they always end up with the exact same result. It turns out to be mathematically impossible to generate true random numbers using a digital computer, but it is fairly easy to generate pseudo-random numbers. This is actually not bad news as pseudo-random numbers -unlike real random numbers- can be generated again and again and you'll end up with the same random numbers every time. Being able to get the same random numbers on demand increases the reliability of these number sequences which in turn makes them easier to use.
Pseudo-random numbers are numbers that have certain characteristics. Note that when we talk about random numbers we are really talking about numbers. Plural. It's easy to generate only a single one, as xkcd so eloquently put it:
So what are these characteristics that define pseudo-randomness? Without being actually correct, I can sum them up as follows:
The sequence of generated numbers should never repeat itself*
The numbers in the sequence ought to be spread evenly across the numeric domain**
There are a lot of different algorithms out there, some better than others, some faster than others, some solving very specific problems while others are more generic. The generator used in Grasshopper is the standard Microsoft .NET Random, based on Donald Knuth's subtractive algorithm.
So let's imagine we want random integers between 0 and 10. What would a bad random sequence look like?
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 (about as bad as it gets)
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 (not random at all)
1 3 2 5 3 9 1 2 4 2 5 1 1 2 8 1 5 2 3 4 (too many low numbers)
2 8 4 6 0 9 8 2 4 8 6 4 2 2 5 1 4 8 6 2 (too many even numbers)
So what about good sequences? Well, here's a few:
6 9 1 2 0 4 2 8 5 7 2 9 1 9 2 5 3 1 9 2 (sure, why not)
6 2 5 3 4 1 9 7 8 0 2 1 6 4 5 8 9 5 0 9 (looks about right)
1 8 5 2 3 4 5 7 9 5 2 1 0 2 1 0 9 7 6 4 (I suppose)
9 0 6 4 8 3 1 5 2 7 6 1 4 6 0 1 9 7 5 6 (whatever)
There are a lot of valid pseudo-random sequences. (Seriously, loads). So even if we have a good pseudo-random generator we may be given a random sequence that isn't entirely to our liking. The shorter the sequence we need, the more likely it is that statistical aberrations invalidate that particular sequence for us. What we need is some control over the generator so we don't just get a repeatable sequence, but a repeatable sequence we actually like.
Enter seed values. The random generator requires a seed value before it can generate a random sequence. These seed values are always integers, and they can be any valid 32-bit integer. Every unique seed value results in the same sequence. Every time.
Unfortunately there is no clear relationship between seeds and sequences. Changing the seed value from 5 to 6 will result in a completely difference random sequence, and two sequences that are very similar may well have to wildly different seeds. There is therefore no way to guess a good seed value, it is completely trial-and-error. Also because of this extremely discontinuous nature, you cannot use tools like Galapagos to optimize a seed value.
If you are looking for a pseudo-random sequence which has custom characteristics, you may well end up having to write your own generator algorithm. Ask questions about this on the Grasshopper main forum or the VB/C# forum.
Conclusion: Seed values are integers that define the exact sequence of pseudo-random numbers, but there's no way of knowing ahead of time what sequence it will be and there's no way of tweaking a sequence by slightly changing the seed. Even the tiniest change in seed value will result in a radically different random sequence.
--
David Rutten
david@mcneel.com
Poprad, Slovakia
* This is not actually possible. A finite amount of numbers always repeats itself eventually.
** This should only be true for long enough sequences, short sequences are allowed to cluster their values somewhat.
Interesting links for further reading:
Coding Horror: Computers are Louse Random Number Generators
StackOverflow: When do random numbers start repeating?…
Added by David Rutten at 9:52am on October 20, 2012
ems in the same way. Lofting was particularly difficult, you had to have a separate loft component for every lofted surface that you wanted to generate because the component would/could only see one large list of inputs. Then came along the data structures in GH v0.6 which allowed for the segregation of multiple input sets.
If you go to Section 8: The Garden of Forking Paths of the Grasshopper Primer 2nd Edition you will find the image above describing the storing of data.
Here you will notice a similarity between the path {0;0;0;0}(N=6) and the pathmapper Mask {A;B;C;D}(i). A is a placeholder for all of the first Branch structures (in this case just 0). B is a place holder for all the second branch structures possibly either 0, 1 or 2 in this case. And so forth.
(i) is a place holder for the index of N. If you think of it like a for loop the i plays the same role. For the example {A;B;C;D}(i) --> {i\3}
{0;0;0;0}(0) --> {0\3} = {0}
{0;0;0;0}(1) --> {1\3} = {0}
{0;0;0;0}(2) --> {2\3} = {0}
{0;0;0;0}(3) --> {3\3} = {1}
{0;0;0;0}(4) --> {4\3} = {1}
{0;0;0;0}(5) --> {5\3} = {1}
{0;0;0;1}(0) --> {0\3} = {0}
{0;0;0;1}(1) --> {1\3} = {0}
{0;0;0;1}(2) --> {2\3} = {0}
{0;0;0;1}(3) --> {3\3} = {1}
{0;0;0;1}(4) --> {4\3} = {1}
{0;0;0;1}(5) --> {5\3} = {1}
{0;0;0;1}(6) --> {6\3} = {2}
{0;0;0;1}(7) --> {7\3} = {2}
{0;0;0;1}(8) --> {8\3} = {2}
...
{0;2;1;1}(8) --> {8\3} = {2}
I'm not entirely sure why you want to do this particular exercise but it goes some way towards describing the process.
The reason for the tidy up: every time the data stream passes through a component that influences the path structure it adds a branch. This can get very unwieldy if you let it go to far. some times I've ended up with structures like {0;0;1;0;0;0;3;0;0;0;14}(N=1) and by remapping the structure to {A;B;C} you get {0;0;1}(N=15) and is much neater to deal with.
If you ever need to see what the structure is there is a component called Param Viewer on the first Tab Param>Special Icon is a tree. It has two modes text and visual double click to switch between the two.
Have a look at this example of three scenarios in three situations to see how the data structure changes depending on what components are doing.
…
.#...
In parameter viewers, we see the number inside the branches remains while going through components (a list of 4 branches of points like {1},{3},{4},{7) put into a polyline component returns an output of polylines with branches {1},{3},{4},{7}).
This was easy to handle, straightforward.
pic2. Grasshopper 0.9.#...
passing through certain components the input branches {1},{3},{4},{7} get "reset" as follow:
{1} becomes {0}, {3} becomes {1}, {4} becomes {2}, {7} becomes {3} etc...
So far the way around this that I know is to replace branches afterwards, but in a real-life GH definition it soon gets extremely fastidious. Not talking about fixing older GH files that get messed up when opened with GH 0.9.#...
Must be a smarter way I'm missing on.
Is there somewhere a setting to get back to the more user friendly GH0.8 way. And some solid reason behind this change?
Thanks.…
Integer = 0 To 9
val *= 2
lst.Add(val)
Next
Since val is a ValueType, when we assign it to the list we actually put a copy of val into the list. Thus, the list contains the following memory layout:
[0] = 2
[1] = 4
[2] = 8
[3] = 16
[4] = 32
[5] = 64
[6] = 128
[7] = 256
[8] = 512
[9] = 1024
Now let's assume we do the same, but with OnLines:
Dim ln As New OnLine(A, B)
Dim lst As New List(Of OnLine)
For i As Integer = 0 To 9
ln.Transform(xform)
lst.Add(ln)
Next
When we declare ln on line 1, it is assigned an address in memory, say "24 Bell Ave." Then we modify that one line over and over, and keep on adding the same address to lst. Thus, the memory layout of lst is now:
[0] = "24 Bell Ave."
[1] = "24 Bell Ave."
[2] = "24 Bell Ave."
[3] = "24 Bell Ave."
[4] = "24 Bell Ave."
[5] = "24 Bell Ave."
[6] = "24 Bell Ave."
[7] = "24 Bell Ave."
[8] = "24 Bell Ave."
[9] = "24 Bell Ave."
To do this properly, we need to create a unique line for every element in lst:
Dim lst As New List(Of OnLine)
For i As Integer = 0 To 9
Dim ln As New OnLine(A, B)
ln.Transform(xform)
lst.Add(ln)
Next
Now, ln is constructed not just once, but whenever the loop runs. And every time it is constructed, a new piece of memory is reserved for it and a new address is created. So now the list memory layout is:
[0] = "24 Bell Ave."
[1] = "12 Pike St."
[2] = "377 The Pines"
[3] = "3670 Woodland Park Ave."
[4] = "99 Zoo Ln."
[5] = "13a District Rd."
[6] = "2 Penny Lane"
[7] = "10 Broadway"
[8] = "225 Franklin Ave."
[9] = "420 Paper St."
--
David Rutten
david@mcneel.com
Poprad, Slovakia…
Added by David Rutten at 6:26am on September 9, 2010