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The Pleasure of Figuring Things Out | Some writings of a mathematical amateurSome writings of a mathematical amateur (by J. M.)
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Some writings of a mathematical amateur (by J. M.)
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The Pleasure of Figuring Things Out. Some writings of a mathematical amateur. February 29, 2012. Still on the matter of Perlin. I finally managed to figure out how to wrap Perlin noise on a sphere (that is, as a. It was a bit inconvenient that it seems (at least, to me) that not one of the usual references on Perlin noise mentioned the explicit formulae needed for a proper spherical embedding of Perlin noise. Making use of the functions already defined in the doc page for. Amp = amplitude},. DensityPlot[...
Yes, I’m still here… | The Pleasure of Figuring Things Out
https://tpfto.wordpress.com/2014/12/21/yes-im-still-here
The Pleasure of Figuring Things Out. Some writings of a mathematical amateur. Yes, I’m still here…. 8230;and to those guys who showed concern and worry during my long-ish absence, I’m fine. Two important things, though: the hard drive containing a lot of my unpublished research crashed, including a good amount that I have not been able to back up; and, I have been quite busy with a (relatively) new job over the past few months, details of which I cannot discuss here. Feed You can leave a response. I am d...
Bunnies, teapots, and noise | The Pleasure of Figuring Things Out
https://tpfto.wordpress.com/2012/03/16/bunnies-teapots-and-noise
The Pleasure of Figuring Things Out. Some writings of a mathematical amateur. Bunnies, teapots, and noise. I should be able to have regular Internet access soon. For now, I’d like to share some of the experiments I did with coloring 3D objects with the help of Ken Perlin’s simplex noise. Relatedly, I’ve found that the implementation of improved Perlin noise supplied in the. Help file has a few subtle flaws, which I was able to fix. That would be for another blog entry, though.). No post-processing at all!
FNV hashing in Mathematica | The Pleasure of Figuring Things Out
https://tpfto.wordpress.com/2012/05/04/fnv-hashing-in-mathematica
The Pleasure of Figuring Things Out. Some writings of a mathematical amateur. FNV hashing in Mathematica. I recently needed to do Fowler/Noll/Vo hashing. I figured other people might be have a need for this hash function as well, so here’s my. FNV hash parameters: bit length, FNV prime, FNV offset *). FNVData = Append[#, Function[{bi, pr},. Fold[BitXor[Mod[pr #1, 2 bi], #2] &, 0,. ToCharacterCode["chongo / ./ "] ] @ #] and /@ Transpose[{2 Range[5, 10],. 2 (8 Quotient[2 Range[5, 10] 5, 12]) 2 8. Fill in y...
On making simulated landscapes | The Pleasure of Figuring Things Out
https://tpfto.wordpress.com/2012/03/01/on-making-simulated-landscapes
The Pleasure of Figuring Things Out. Some writings of a mathematical amateur. On making simulated landscapes. This entry is based on an idea by Paul Bourke. For generating simulated landscapes through the application of the two-dimensional discrete Fourier transform to an array of uniformly-distributed random numbers. I was also inspired by some of the color gradients featured in GRASS. I wanted to try it out on a simpler function first, and decided to use the. As a test case:. Not too shabby, eh? The re...
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Mathematica bits: Magic Square
http://mathematica-bits.blogspot.com/2011/01/magic-square.html
Tips for Mathematica users. Sunday, January 2, 2011. Here's an interesting tidbit I saw linked. From reddit - the following decimal expansions form a magic square. Here's how you'd check the row and column sums. Row[k ] := PadLeft[IntegerDigits[Floor[k/(v 1)*10 v] , v];. Mat = row /@ Range[v];. Posted by Yaroslav Bulatov. October 4, 2014 at 12:04 PM. Its a great posting. Thank you for sharing with us. Subscribe to: Post Comments (Atom). The Pleasure of Figuring Things Out. Can you help me?
Mathematica bits: Semidefinite programming in Mathematica using CVXOPT
http://mathematica-bits.blogspot.com/2011/03/semidefinite-programming-in-mathematica.html
Tips for Mathematica users. Thursday, March 3, 2011. Semidefinite programming in Mathematica using CVXOPT. One can get access to semidefinite programming from Mathematica by using Pythonika to interface with Python's cvxopt package. For MacOS 10.6 and Mathematica 8 the following should work. Install 64-bit Python 2.7 distribution from official site. Get latest cvxopt sources. Fill correct paths in Pythonika Makefile, also add "-lstdc -framework CoreFoundation" linker flags. G = GridGraph[{4, 3}];. Gram =...
Mathematica bits: Independence Polynomials with Tree Decomposition
http://mathematica-bits.blogspot.com/2011/01/independence-polynomials-with-tree.html
Tips for Mathematica users. Saturday, January 8, 2011. Independence Polynomials with Tree Decomposition. A lot of NP-hard problems on graphs become easy if you find a good tree decomposition. Essentially, tree decomposition asks for a way to take a set of small sets of vertices and connect them in a way so that vertices shared by any pair of connected sets is a separator of the graph. Two examples below show a graph on the left and it's optimal tree decomposition on the right. Posted by Yaroslav Bulatov.
Mathematica bits: Making cross-words with Mathematica
http://mathematica-bits.blogspot.com/2011/02/making-cross-words-with-mathematica.html
Tips for Mathematica users. Wednesday, February 2, 2011. Making cross-words with Mathematica. A recent question on Stack Overflow. Asked how to use Mathematica to find a complete grid of words like this. Each row and each column must be a valid word. A notebook below gives a way to solve this for small grids using SAT solver, and another answer in the post gives a pattern-based approach. Posted by Yaroslav Bulatov. October 4, 2014 at 11:53 AM. Subscribe to: Post Comments (Atom). Can you help me?
Mathematica bits: Cluster variation method example
http://mathematica-bits.blogspot.com/2011/02/cluster-variation-method-example.html
Tips for Mathematica users. Monday, February 7, 2011. Cluster variation method example. Cluster variation methods for search work by approximating the distribution over satisfying instances, and then using marginals of that distribution to guide the search. Here's an animation of occupation probability marginals with lambda going from 0 to 3. You can see the mass gets concentrated on nodes that are part of the largest independent set in the graph, at which point you can use greedy search. Can you help me?
Mathematica bits: Coloring overlapping circles
http://mathematica-bits.blogspot.com/2011/01/coloring-overlapping-circles.html
Tips for Mathematica users. Saturday, January 15, 2011. Take some overlapping circles. Ineqs = Table[(x - 2/3 Cos[i 2 Pi/nc]) 2 (y -. 2/3 Sin[i 2 Pi/nc]) 2. RegionPlot[ineqs[ k] , {x, -2, 2}, {y, -2, 2}, PlotPoints - 35,. PlotStyle - Opacity[.2] , {k, 1, nc}]. What if we want to color overlapping regions according to how many overlaps they had? We can use "BooleanCountingFunction" as follows. BooleanCountingFunction[{k}, ineqs], {x, -2, 2}, {y, -2, 2},. PlotPoints - 100, Frame - None,. Can you help me?
Mathematica bits: Visualizing SDP cone
http://mathematica-bits.blogspot.com/2012/01/visualizing-sdp-cone.html
Tips for Mathematica users. Monday, January 30, 2012. One way to visualize cone of positive semi-definite matrices is to take random 2D sections of the cone. Example is below, from images it's clear this region is non-smooth. It doesn't look as instructive in 3D, but for example of doing the same in 3D, see this Mathematica stackexchange post. Posted by Yaroslav Bulatov. January 31, 2012 at 2:15 PM. I have a couple questions:. 1 Why do you add the identity matrix when defining mat2? Adding identity matri...
Mathematica bits: Tree decomposition package
http://mathematica-bits.blogspot.com/2011/01/tree-decomposition-package.html
Tips for Mathematica users. Friday, January 21, 2011. A tree decomposition is a representation of a complete set of vertex separators of a graph. For instance, here's an Apollonian Network. And its tree decomposition. Decomposition above shows off 121 vertex separators of size 4, represented as non-leaf nodes, each separating graph into 3 parts, and 363 vertex separators of size 3, represented as edges, each separating the graph into 2 parts. G = GraphData[{"Apollonian", 5}];. GraphPlot[Rule @ @ edges].
Mathematica bits: Chordal graph utilities
http://mathematica-bits.blogspot.com/2011/02/chordal-graph-utilities.html
Tips for Mathematica users. Tuesday, February 8, 2011. Here's visualization of a matrix and its Cholesky factorization. The sparsity pattern in the Cholesky factorization corresponds to the adjacency matrix of the graph triangulated using canonical ordering. This triangulation involves adding so called "fill" edges and can be visualized below. Consider the following matrix and its Cholesky decomposition. Order = getMinFillOrder[AdjacencyGraph@Unitize@A];. Here's an example of a structured sparse matrix a...
Mathematica bits: Mathematica Stack Exchange launched
http://mathematica-bits.blogspot.com/2012/01/mathematica-stack-exchange-launched.html
Tips for Mathematica users. Monday, January 30, 2012. Mathematica Stack Exchange launched. After more than a year, the proposal for separate Mathematica stack exchange platform has been approved, and the site has been launched. Http:/ mathematica.stackexchange.com/ So far it seems quite active, and I was able to get my question answered within minutes. Posted by Yaroslav Bulatov. October 4, 2014 at 11:18 AM. Subscribe to: Post Comments (Atom). Lunchtime Playground: Fun with Mathematica.
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The Pleasure of Figuring Things Out | Some writings of a mathematical amateur
The Pleasure of Figuring Things Out. Some writings of a mathematical amateur. Yes, I’m still here…. December 21, 2014. 8230;and to those guys who showed concern and worry during my long-ish absence, I’m fine. Two important things, though: the hard drive containing a lot of my unpublished research crashed, including a good amount that I have not been able to back up; and, I have been quite busy with a (relatively) new job over the past few months, details of which I cannot discuss here. Posted by J. M.
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