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heh, I'd rather development effort be put into getting the Linux RRing tools mature, rather than developing for a platform that any self respecting person would never use.
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If you use FRAPs, it takes an image of the emulation, which means that the movie will be unreproducible on an emulator by conventional methods.
Which means that we'll be unable to accept the video here.
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LSK wrote:
I made an unoptimized runthrough of the GBA version as a jumping-off point. It's about 1:45; there are maybe 15 minutes of improvements that can be made. There are a few different cage locations, though. I'm posting this in the GBA forum too.
Link
It seems that phpBB doesn't like your link thar.
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Set a man on fire, warm him for the rest of his life.
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Some findings,
The algorithm seems imperfect for progression lengths that have chaotic behavior. These are generally odd values; however, values of 8 and 14 also exhibit this behavior. (Only have tested values up to 18.)
This is what I have thus far plotted against the harmonic series. From the bottom up are all of the well behaved progression values (chaotic ones sum up to less than expected, and therefore the algorithm used to generate them is flawed.)
We are probably dealing with the difference between divergent and convergent series, so it's unsurprising how slowly everything seems to converge. I kinda want to try, just for kicks, a very large progression value and plot it against the harmonic series, when I'm done with these current jobs.
From bottom, 2, 4, 6, 10, 12, 16, 18, harmonic
I'm currently running these until they reach 1 million terms.
Here's some numerical results.
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scwizard wrote:
Kejardon wrote:
but then I don't think Samus can get out before the timebomb's up
How the heck would you get past the doors that close on you at the beginning without the hyper beam (or the morphball or anything else).
Unless you're given the hyper beam despite not fighting mother brain.
And if you have the hyper beam, what are the difficulties in getting out?
Those doors are designed to explode from any shot. You just always happen to have the Hyper beam when encountering them.
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Ignoring arithmetic progressions of 0. The even progression lengths behave regularly, and the odds... don't.
The even ones seem to converge up to n+1 where n is the progression length.
The odd numbers.... don't.
I've wrote a program to generate arithmetic progressions the same way that you described. (Proving it generates the densest set is a different matter, of course.) And I let it run over night.
For progression length 2, it's converged very quickly on 3.
For progression length 3, it is converging very very slowly on a number at least 4.2623
I just tailed the results and that's what I get, the columns are current member of the series, current series length, difference between the current member and the last member, and the sum total.
I haven't a clue when it's going to stabilize out.
If anyone cares to run it on a faster computer, here's the code I wrote, it's a little hackish, but well optimized.
#include <iostream>
#include <iomanip>
int main() {
int series[1000000]; //we can change this later if we need more computingness.
series[0] = 1;
int series_length = 1;
int length_arith_prog = 3;
double sum = 1.0;
int n = 2;
std::cout << std::setprecision(20);
for (;;n++) {
int found = 0;
for (int i=0; i < series_length && found == 0; i++) {
int members_arith_prog = 0;
int debug = (n - series[i])%length_arith_prog;
if (!((n - series[i])%length_arith_prog)) { //if between these two numbers it is possible to have an arithmetic progression of the specified length
int common_diff = (n - series[i])/length_arith_prog;
for (int j=1; j < length_arith_prog; j++) {
/* for (int k=i+1; k < series_length; k++) { //we only want to test numbers larger than the one we're currently examining.
if (series[k] == series[i] + j*common_diff) {
members_arith_prog++;
}
}*/
int mid=((i+1)+(series_length-1))/2; //the +1 and -1 cancel, they're just there to remind me.
int high = series_length;
int low = i+1;
int value = series[i] + j*common_diff;
while (low < high) {
mid = low + ((high - low) / 2); // Note: not (low + high) / 2 !!
if (series[mid] < value) {
low = mid + 1;
} else {
high = mid;
}
}
if ((low < series_length) && (series[low] == value)) {
members_arith_prog++;
}
}
}
if (members_arith_prog+1 == length_arith_prog) { //found a arithmetic progression!
found = 1;
}
}
if (found == 0) {
series[series_length] = n;
int deriv = series[series_length] - series[series_length-1];
series_length++;
sum += (1.0/n);
std::cout << n << " " << series_length << " " << std::setw(5) << deriv << " " << sum << std::endl;
}
}
}
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This evening I looked into the Erdos conjecture on arithmetic progressions and attempted to prove the contrapositive by attempting to place an upper bound on series with various progression lengths.
So here's a few challenges that arose out of that.
1. Given the following series:
1/1+1/1+1/2+1/2+1/4+1/4+1/5+1/5+1/10+1/10+1/11+1/11+1/13+1/13+1/14+1/14+1/28+1/28+1/29+1/29+1/31+1/31+1/32+1/32+1/37+1/37+1/38+1/38+1/40+1/40+1/41+1/41+1/82+1/82+ ...
(Why doubled? Because arithmetic progressions of common difference 0 count too.)
Prove this that series converges to the highest possible value that any series of whole number reciprocals can without containing an arithmetic progression with a length greater than 2. (When I say length greater than n I mean the arithmetic progression does not contain more than n members.)
2. What is the series of whole number reciprocals that do not contain an arithmetic progression with a length greater than 3 that converges to the highest possible value?
3. It seems that some of these series have regular, patterned and self symmetric behavior and others have quite chaotic behavior, any clue as to how to predict this?
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Nes Video Agent / Calc
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Build a man a fire, warm him for a day,
Set a man on fire, warm him for the rest of his life.
This is what I have thus far plotted against the harmonic series. From the bottom up are all of the well behaved progression values (chaotic ones sum up to less than expected, and therefore the algorithm used to generate them is flawed.)
We are probably dealing with the difference between divergent and convergent series, so it's unsurprising how slowly everything seems to converge. I kinda want to try, just for kicks, a very large progression value and plot it against the harmonic series, when I'm done with these current jobs.
From bottom, 2, 4, 6, 10, 12, 16, 18, harmonic
I'm currently running these until they reach 1 million terms.
Here's some numerical results.