13 5 15 6 17 7 ... …
But it seems I have not been clear:
the input values (3,5,7,9,11,13) should be presented in the way of "number slider" parameter. So by increasing the value of the slider from minimum 3, to 5, 7, 9, 13, 15, 17... I should get an output numbers of 0,1,3,4,5,6,7...
So I if choose value 3 on the input "number slider", on the other end, I want 0 as an output.
Or if I choose value 5 on the input "number slider", I want 1 as an output, and so on.
Is this possible?…
where each branch contains all the points generated by dividing each curve, so if you divide into 10 segments, you'll get:
{0;0}(N = 11)
{0;1}(N = 11)
{0;2}(N = 11)
{0;3}(N = 11)
{0;4}(N = 11)
Where the second integer in the curly brackets refers back to the index of the curve in the original list.
Another way to look at this data is to see it as a table. It's got 5 rows (one for each original curve) and 11 columns, where every column contains a specific division point.
--
David Rutten
david@mcneel.com
Poprad, Slovakia…
This must be a bug because its true for dividing by all odd numbers:
(i-1)/3
(i-2)/5
(i-3)/7
(i-4)/9
(i-5)/11
....
(i-n)/2n+1
And you can't make it work for even numbers
Added by Danny Boyes at 5:06pm on January 13, 2010
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
、、、不同角度的理解、诠释、运用和发掘规律、、、
新闻或者幻觉:马王堆墓穴中发掘出了丝绸做的鞋,不算是现代意义上真正的鞋,但是完成了一个完整的公式。
有一部分需要是共同的,在离开了沙滩和草地的时候。
找一个成熟的不一样的数学思维合作者,(可以一起申请参加sg2014活动,也可以不)
我想听到人们写给自己的语言,我不害怕听不懂;
也不在意你能看到我的美丽的脚和我们美丽的城市。
你存在?存在0.1%?如果≥1/4
With the two version of the PDF in the file upload, doubt, 10th should be able to see the many PDF.
There are some scruples, confusion ——"The additional property of professional activities",——Subject classification, commercial, regional、、、
There is a place Africa, people don't wear shoes, A few people with grass or leather on the foot (and buildings——In order to spatial density) winding,
the manufacture of shoes, two sales do two judgment:
A There is no life belongs to shoes
B this is the market.
I spent a lot of energy explained to students, which is not to do programming people do、、、 the different angle understanding, interpretation, application and explore the law、、、
The news or illusion:Mawangdui tomb unearthed silk shoes , is not the modern sense of true shoes, but the completion of a complete formula.
There is a need is common, when they leave the beach and grass.
Find a mathematically mature different thinking partners,(Can apply to participate in the activities of the sg2014, also can not)
I want to hear people wrote their own language, I am not afraid of don't understand;
Don't care what you can see my beautiful feet and our beautiful city.
Do you have? There are 0.1%? If ≥1 / 4 You know what I did wheni found out about you?
msxf6688@163.com
…