Tag: mathematical visualization

Another Graph Paper Tiling
Advertisements Below is the beginning of a second QuasiPenrose tiling I’ve made using virtual graph paper and an irregular pentagon created and flipped thereon.

The Odd Integers 3 Through 129
Advertisements Arranged as Red Squares on a Square Grid Artistically Arranged According to Their DifferencesofSquares Expression Based on Their Ceiling Squares

More Visualization
Advertisements Here are icons for the odd integers from 3 to 65, based on the differences of each with their ceiling squares (the smallest perfect square greater than their value). The integer corresponding to an icon is the number of red 1×1 squares in that icon.

Today’s Mathematical Visualization
Advertisements This is an artistically arranged gridbased drawing of the first 24 odd integers greater than 1, expressed as differences of squares – to include the first odd positive integer to have two different “nontrivial” factorizations, and thus two different squaredifference representations.

Adjusted Scatter Plot for Integer Factorization Study
Advertisements The plot below is similar to the one I put in my previous post. However, the data points are, I think, a better set for exposing properties, since I am using the concept of Adjusted Ceiling Square as follows: Let m be an odd positive integer. Define the Adjusted Ceiling Square of m as…

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…