archery: Archive

4 tags

Watch

Music: “Parisian Goldfish (Take Remix)” by Flying Lotus Watch the rest of the video in sub-par quality here. When it comes to the rapid movement of unnaturally bright colors Tumblr’s video transcoding seems to work better than both Vimeo’s and YouTube’s! Mathematica code: ListAnimate[ Table[ ImageCrop[ DensityPlot[ Sin[(t*.005)*Abs[(x + I y)^2]], {x, -8,...

Mar 29th

8 notes

4 tags

Mathematica code: f[x_, y_] := {Log[Sqrt[(x)^2 + (y)^2]], ArcTan[x, y]} ListAnimate[ Table[ ImageTransformation[ ImageResize[ImageTake[ImageCrop[ DensityPlot[ Sin[104.02*Abs[(x + I y)^2]], {x, -4.26, 4.26}, {y, -4.26, 4.26}, PlotPoints -> 27, Mesh -> False, Frame -> False, ColorFunction -> Hue, ImageSize -> 834], 800], {193 - t, 747...

Mar 28th

58 notes

3 tags

Mar 28th

16 notes

5 tags

Mar 27th

236 notes

3 tags

Mar 27th

82 notes

5 tags

Mar 26th

482 notes

4 tags

Mar 26th

7 notes

2 tags

Mar 26th

8 notes

1 tag

Mar 24th

44 notes

2 tags

Math book recommendations

Recommend books about mathematics. I am specifically interested in books for the layperson, but books at other levels are fine too. Perhaps you could mention the reading level (something like “for anyone”, “basic math background”, “advanced”). ?

Mar 24th

28 notes

2 tags

sicut-erat-in-principio asked: Can you recommend me some good books about mathematics? thanks!

Mar 24th

11 notes

3 tags

Anonymous asked: Did you choose this coordinate transformation at random or is the position of the neurons in V1 in someway a basis for this transition?

Mar 24th

2 notes

4 tags

Mar 23rd

220 notes

4 tags

Mar 23rd

22 notes

4 tags

Mar 23rd

32 notes

5 tags

Mar 23rd

29 notes

5 tags

Mar 23rd

30 notes

6 tags

Mar 23rd

339 notes

8 tags

Visual Hallucinations and Form Constants

Whether or not you know about or care to use the mathematical coordinate systems described in the last post, it seems that our eyes and brains already make use of them when seeing and hallucinating. How this is the case will be explained here in some detail. Of course, our senses are intricately correlated with the dynamics of our brains in ways so complex that we can barely understand or even...

Mar 23rd

522 notes

7 tags

Coordinate Systems - Cartesian and Polar

For the purpose of describing something, sometimes its useful to have a systematic way to label the relevant parts of that thing. In mathematics, things such as curves, surfaces, and abstract spaces in general can be described using what are called coordinate systems. A familiar example of such a coordinate system may be the standard way points are described in the two-dimensional real plane. This...

Mar 16th

46 notes

4 tags

Mar 15th

27 notes

4 tags

Mar 15th

37 notes

3 tags

Mar 15th

33 notes

4 tags

Mar 15th

21 notes

6 tags

Mar 14th

29 notes

5 tags

Mar 14th

30 notes

5 tags

Mar 14th

91 notes

5 tags

Mar 12th

30 notes

5 tags

Mar 12th

12 notes

3 tags

Mar 10th

175 notes

4 tags

Mathematica code: Animate[ DensityPlot[ Sum[.20*Cos[(Cos[n*2*Pi/5] + Sin[n*2*Pi/5])*x + (Cos[n*2*Pi/5] - Sin[n*2*Pi/5])*y + t]^10, {n, 0, 4, 1}], {x, -25, 25}, {y, -25, 25}, PlotPoints -> 50, Mesh -> False, Frame -> False, ColorFunction -> GrayLevel, ImageSize -> 521], {t, 0, 2*Pi, Pi/20}]

Mar 10th

41 notes

3 tags

Mathematica code: Animate[ DensityPlot[ Sum[.20*Cos[(Cos[n*2*Pi/5] + Sin[n*2*Pi/5])*x + (Cos[n*2*Pi/5] - Sin[n*2*Pi/5])*y + t]^10, {n, 0, 4, 1}], {x, -25, 25}, {y, -25, 25}, PlotPoints -> 50, Mesh -> False, Frame -> False, ColorFunction -> GrayLevel, ImageSize -> 521], {t, 0, 2*Pi, Pi/20}]

Mar 10th

8 notes

6 tags