The density of bonuses is not constant at all. There are some places with a higher density. Now, assume I was a bigger point and my knowledge about the distribution of bonuses was complete. Of course I would prefer to be at places with a higher density. But there is a parameter that affects my decisions! And that is "I am not alone in the world, there are other points that can eat those bonuses" and each point wants every thing for itself and is never satisfied. I want to eat as much as I can!
As it is obvious the smaller the other points are, the more I can eat. So I should try to prevent other points from getting bigger. But what should be the solution? I know the points close to places with a high density are the more dangerous ones. They are the axis of evil and if I let them live they will get bigger faster than others. What should be the solution?
1- Let's accept that anyway those points will get bigger. I will find as many bonus as I can and let them live ther. In this solution I am always living at places with a higher density, and also there are some rivals that have got bigger and now they are eating with an equal rate comparing to me. but we are big.
2- I can start iterating among the high density places. just to eat the envirnoment around the smaller points but very fast, just around those points to prevent them from eating until I will be back there in the next round. This seems very smart! It is more effiecient comparing to the previous solution.
3- Of course the second solution is much better than the first one but it is not always the best solution. What will happen if my speed is not enough to be able to eat the bonuses around all small points around higher density places? Some of them will have chance to eat bonuses! I hate this. but often if you think you can find another trick!
I have a suggestion. lets find a friend. Maybe if we were two big points we were enough to eat all around:D So I will let one of those small points to get big but only that one. We are friends and there is enough points for both of us. My friends' number is equal to how many friends do I need! This was one of the rules that the painter discovered at very beginning!
Saturday, December 16, 2006
Friday, December 15, 2006
What is the definition of satisfaction?
So again lets go back and think about the goal!?
I say the goal is, to reach the maximum available amount of satisfaction for the whole system. Satisfaction for the whole system is computed by adding the satisfaction amounts for each individual point. Though now the word 'satisfaction' has to be determined. What does that mean?
I say a point is more satisfied if it is bigger! How a point can get bigger? Of course, each point get bigger by eating a bonus. How a point can eat a bonus? by moving. Also as I mentioned in the previous post each point creates bonus by moving, these bonuses actually decrease the point's weight. So a point prefers to move in a direction that there are more bonuses! I mean if a point wants to move in a direction that there is no point, it will just lose weight, but if there are enough points that worth moving it should prefer to move. So after running the system for a while I guess the density and weight of the points will be higher around the places with a higher density of bonuses.
Now lets start thinking about more specific conditions.
Suppose the density of bonuses is constant all over the paper. Suppose there is a very big point and some small points. What will happen?
Lets imagine all the points start moving with a similar speed. The amount of bonuses the bigger point eats in an interval should be greater than the bonus eated by smaller points. So the bigger the point is the faster the growth rate will be. Also when the bigger point moves more bonus is produced which maybe if I were a smaller point I could just keep following the bigger one. because I would be sure that always there will be enough bonus created for me by that bigger one. There maybe cases that there is no bonus around, and the bigger one is moving to find bonuses, if I am a smaller point and following that big one, even if it is not eating it is available for me to eat because it is moving and producing bonus.
I say the goal is, to reach the maximum available amount of satisfaction for the whole system. Satisfaction for the whole system is computed by adding the satisfaction amounts for each individual point. Though now the word 'satisfaction' has to be determined. What does that mean?
I say a point is more satisfied if it is bigger! How a point can get bigger? Of course, each point get bigger by eating a bonus. How a point can eat a bonus? by moving. Also as I mentioned in the previous post each point creates bonus by moving, these bonuses actually decrease the point's weight. So a point prefers to move in a direction that there are more bonuses! I mean if a point wants to move in a direction that there is no point, it will just lose weight, but if there are enough points that worth moving it should prefer to move. So after running the system for a while I guess the density and weight of the points will be higher around the places with a higher density of bonuses.
Now lets start thinking about more specific conditions.
Suppose the density of bonuses is constant all over the paper. Suppose there is a very big point and some small points. What will happen?
Lets imagine all the points start moving with a similar speed. The amount of bonuses the bigger point eats in an interval should be greater than the bonus eated by smaller points. So the bigger the point is the faster the growth rate will be. Also when the bigger point moves more bonus is produced which maybe if I were a smaller point I could just keep following the bigger one. because I would be sure that always there will be enough bonus created for me by that bigger one. There maybe cases that there is no bonus around, and the bigger one is moving to find bonuses, if I am a smaller point and following that big one, even if it is not eating it is available for me to eat because it is moving and producing bonus.
Thursday, December 14, 2006
More Specification
Yeah,
The painter had two markers. A yellow one and a brown one. Each point could be either yellow or brown! The greater rule is that the brown and yellow points can match to make a small cluster. There are clusters in different layers. Each point has some attributes that identify the cluster it will fall in. Each cluster is moving in a different way. The movement direction of a cluster is calculated easily by adding the movements of individual points. Usually we can assume a normal distribution on every attribute inside a cluster. but this is not always the case. for example for the variable "beautiful", each point can get a value between 0 to 1. If the distribution is normal, most of the points will get a value around 0.5. but always the system can have some embedded noise. I call a point with a value equal to 1 noise as like as a point with a value equal to 0.
Points started to look around! They was courious to know more about whole paper which they are allocated on. So they started to move. Some of the characteristics of the points are listed here:
1- A point is never satisfied. It always wants more.
2- A point wants every thing for itself. Even it will fuck others to catch what it wants.
3- A brown point needs to be with a yellow one. This is also true for yellow ones.
4- Brown points are completely different from yellow ones. They have totaly different emotions. For example a yellow one wants a brown point to enjoy being with each other, but a brown point wants to be with a yellow one to enjoy the yellow one!
5- There are some bonuses all around. Each point can get bigger by eating a bonus.
6- Each point can eat bonuses while moving. eating a bonus causes increase in weight. Also each point can make bonuses by moving. The bigger the point is, the more bonus is generated when it moves.
Imagining these facts, now we are going to analyse this system in next posts;)
The painter had two markers. A yellow one and a brown one. Each point could be either yellow or brown! The greater rule is that the brown and yellow points can match to make a small cluster. There are clusters in different layers. Each point has some attributes that identify the cluster it will fall in. Each cluster is moving in a different way. The movement direction of a cluster is calculated easily by adding the movements of individual points. Usually we can assume a normal distribution on every attribute inside a cluster. but this is not always the case. for example for the variable "beautiful", each point can get a value between 0 to 1. If the distribution is normal, most of the points will get a value around 0.5. but always the system can have some embedded noise. I call a point with a value equal to 1 noise as like as a point with a value equal to 0.
Points started to look around! They was courious to know more about whole paper which they are allocated on. So they started to move. Some of the characteristics of the points are listed here:
1- A point is never satisfied. It always wants more.
2- A point wants every thing for itself. Even it will fuck others to catch what it wants.
3- A brown point needs to be with a yellow one. This is also true for yellow ones.
4- Brown points are completely different from yellow ones. They have totaly different emotions. For example a yellow one wants a brown point to enjoy being with each other, but a brown point wants to be with a yellow one to enjoy the yellow one!
5- There are some bonuses all around. Each point can get bigger by eating a bonus.
6- Each point can eat bonuses while moving. eating a bonus causes increase in weight. Also each point can make bonuses by moving. The bigger the point is, the more bonus is generated when it moves.
Imagining these facts, now we are going to analyse this system in next posts;)
What is the goal?
Once upon a time, A painter decided to draw some points on a large piece of paper. But it was not like regular ones. When he drew some points, he started getting tired. He found it boring. He decided to give each point a name. Cool! It was more interesting. He continued drawing points. All the points were similar the only difference was their position in that sheet. So each point were uniquely specified by its x and y coordinates. After painting a millions of points just again he found it boring. It was like a dead dotted piece of sheet! To get rid of that death condition he added a feature. He letted points to move. He said: "Each of you go and live on this paper. you can move. you can make clusters. you can delete others or create others. you can find others. you can fall in love with others. you can move. and you can decide on your self where you want to move. you can be a good point and let other points to be happy or you can be a bad point and disappoint me. But this is what I have maid and no body is going to change it". He said that. Then he left.
Nowadays, Some times he comes back to take a look to see what's going on there. All the points are bored, they are waiting for a new point to change the conditions. They think there will be a day that a point will make all the clusters one. And will make all the points happy. No one knows about that ones coordinates.
But what was the painters goal? Maybe he prefered a dotted paper to a plain one. Maybe he had just that paper. Maybe he wanted to do something fair, and the only solution was to draw points. Maybe he was looking to a new life.
Nowadays, Some times he comes back to take a look to see what's going on there. All the points are bored, they are waiting for a new point to change the conditions. They think there will be a day that a point will make all the clusters one. And will make all the points happy. No one knows about that ones coordinates.
But what was the painters goal? Maybe he prefered a dotted paper to a plain one. Maybe he had just that paper. Maybe he wanted to do something fair, and the only solution was to draw points. Maybe he was looking to a new life.
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