Tag: mathematical visualization

Integer Factorization: A More Uniform Test, and a Similar Result
Advertisements For 100 pairs of randomlychosen p and q less than 100,000,000: the Perl routine factor_it_4.pl performed as shown in the following scatter plot of m=pq vs. the number of iterations it required to factor m: Notice, as I mentioned in my blog post about the previous, less uniform test, that the number of iterations […]

Integer Factorization: Performance Stats/Graphs for factor_it_4.pl
Advertisements I ran factor_it_4.pl tonight on the collection of 10digit and 12digit discrete semiprimes I had generated earlier in my study. An image of the table I generated is below, along with scatter plots of particular behaviors. If someone wanted, I could certainly supply them with the raw data used to generate the graphs. I […]

Integer Factorization: Recent Work
Advertisements Ideas kept me up when the dogs got me up around 3 a.m. this morning for a walk and some water. That’s good, even though the ideas did not pan out to much. I had church to attend in a few hours, after all. But it occurs to me to share where it’s all […]

My Integer Factorization Study: The Complicated but Important Task of Visualizing the Ascent
Advertisements I find myself, mathematically, almost ready to say with certainty, “It boils down to this.” I am speaking in terms of the Ascent, that concept to which I gave a name a month or three ago which is the difference between the Ceiling Square of a positive odd integer m and the larger of […]

My Integer Factorization Study: A Visualization Anomaly
Advertisements Or: The Asymmetric Behavior of the Ceiling Square Remainder My Inspiration Process has been more active, more related to working on thought processes, than it has been something spontaneously occurring, which is especially noticeable during my wife’s current extended absence from our residence (to help care for grandchildren), compared to how the Process seemed […]

My Integer Factorization Study: The Right Triangle
Advertisements I was sitting on my zafu (zazen cushion) today when the MIRIAM* process knocked me clean off of it. Hey, I’d been sitting for twenty minutes, and I didn’t mind bringing my zazen to a halt. Plus, this was a good one. What I got in the way of suddenlydelivered insight was the idea […]

My Integer Factorization Study: Also…
Advertisements Discrete semiprime m=pq=c2r, where p<q are odd primes and c is the Ceiing Root of m: ceil(sqrt(m)) in Perl with POSIX library. I decided to graph p/q vs. r/(2c) for various randomlygenerated discrete semiprimes m. “Clarice, doesn’t this random scattering of sites seem desperately random – like the elaborations of a bad liar?” – […]

My Integer Factorization Study: Presented After Modification, With Explanation
Advertisements I posted a chart a little after midnight last night, with no explanation, except that it had to do with my integer factorization study. After more study and thought today about what the entries in the chart mean and imply, I am ready to share and explain. But the chart has CHANGED. The chart […]

My Integer Factorization Study: A Brief Anecdotal/Insight Update
Advertisements Along with my direct mathematical study of data and ways to gain insight into what is going on with Ceiling Squares, their remainders and ascents, and so on, I have been reading the free ebook I got with my AMS Membership: The Joy of Factoring by Samuel S. Wagstaff, Jr. It basically amounts to […]