intothecontinuum: Inspired by Vasilj Godzh Mathematica code: s[q_] := (SeedRandom[q]; RandomReal[])r[S_, a_, v_, w_, t_] := S (1 + .05 Sin[v*a] Cos[w*a] + .1 Cos[8*a] + .025 Sin[a + t])F[Q_, S_, M_, v_, w_, th_, t_] := {EdgeForm[{AbsoluteThickness[th], Black}], FaceForm[White], Polygon[ Table[ {{0, 0}, {r[S, (a + s[Q*a]) 2 Pi/M, v, w, t] Cos[(a + s[Q*a]) 2 Pi/M], r[S, (a + s[Q*a]) 2 Pi/M, v, w, t] Sin[(a + s[Q*a]) 2 Pi/M]}, {r[S, (a + 1 + s[Q (Mod[a, M] + 1)]) 2 Pi/M, v, w, t] Cos[(a + 1 + s[Q (Mod[a, M] + 1)]) 2 Pi/M], r[S, (a + 1 + s[Q (Mod[a, M] + 1)]) 2 Pi/M, v, w, t] Sin[(a + 1 + s[Q (Mod[a, M] + 1)]) 2 Pi/M]}}, {a, 1, M, 1}]]}Manipulate[ Graphics[ Table[ Translate[ Reverse@ Table[ F[i*j, (1 + .3 i^1.7), 125 + 25 i, 3 + Round[9 s[i*j]], 3 + Round[9 s[2 i*j]], .6, t + s[j] 2 Pi], {i, 1, 4, 1}], {17*s[j], 23.8*s[2 j]}], {j, 1, 46, 1}], PlotRange -> {{.5, 17.5}, {-1.2, 22.6}}, ImageSize -> {500, 700}], {t, 0, 2Pi}]
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intothecontinuum:

Inspired by Vasilj Godzh

Mathematica code:

s[q_] := (SeedRandom[q]; RandomReal[])

r[S_, a_, v_, w_, t_] := 
 S (1 + .05 Sin[v*a] Cos[w*a] + .1 Cos[8*a] + .025 Sin[a + t])

F[Q_, S_, M_, v_, w_, th_, t_] :=
 {EdgeForm[{AbsoluteThickness[th], Black}], FaceForm[White],
  Polygon[
   Table[
    {{0, 0},
     {r[S, (a + s[Q*a]) 2 Pi/M, v, w, t] Cos[(a + s[Q*a]) 2 Pi/M],
      r[S, (a + s[Q*a]) 2 Pi/M, v, w, t] Sin[(a + s[Q*a]) 2 Pi/M]},
     {r[S, (a + 1 + s[Q (Mod[a, M] + 1)]) 2 Pi/M, v, w, t] Cos[(a + 1 + s[Q (Mod[a, M] + 1)]) 2 Pi/M],
      r[S, (a + 1 + s[Q (Mod[a, M] + 1)]) 2 Pi/M, v, w, t] Sin[(a + 1 + s[Q (Mod[a, M] + 1)]) 2 Pi/M]}},
    {a, 1, M, 1}]]}

Manipulate[
 Graphics[
  Table[
   Translate[
    Reverse@
     Table[
      F[i*j, (1 + .3 i^1.7), 125 + 25 i, 
         3 + Round[9 s[i*j]], 3 + Round[9 s[2 i*j]],
        .6, t + s[j] 2 Pi],
      {i, 1, 4, 1}],
    {17*s[j], 23.8*s[2 j]}],
   {j, 1, 46, 1}],
  PlotRange -> {{.5, 17.5}, {-1.2, 22.6}}, 
  ImageSize -> {500, 700}],
 {t, 0, 2Pi}]
intothecontinuum: Mathematica code:Rot80 = Table[ Table[ RotationTransform[a, {1, 1, 0}, {0, 0, 0}][Tuples[{-1, 1}, 3][[v]]], {v, 1, 8, 1}],{a, 0, 2 Pi, Pi/80}]Edge := {1, 2, 4, 3, 7, 8, 6, 5, 1, 3, 4, 8, 7, 5, 6, 2}CubeTrail[h_, op_, N_, s_, r_, z_, t_, PR_, IS_, C_] := Graphics[ Table[ Scale[ Translate[ {AbsoluteThickness[h], Opacity[op], If[C == 1, Black, White], Line[ Table[ {Rot80[[1 + Mod[t, 80]]][[Edge[[e]]]][[1]], Rot80[[1 + Mod[t, 80]]][[Edge[[e]]]][[2]]}, {e, 1, 16, 1}]]}, r{Cos[2 Pi*(n*t/80 + k)/N], Sin[2 Pi*(n*t/80 + k)/N]}], z^n, r{Cos[2 Pi*(n*t/80 + k)/N], Sin[2 Pi*(n*t/80 + k)/N]}], {k, 1, N, 1}, {n, 1, s, 1}], PlotRange -> PR, ImageSize -> 500, Background -> If[C == 0, Black, White]]Manipulate[P = {h, op, N, s, r, z, t, PR, IS, C}; CubeTrail[h, op, N, s, r, z, t, PR, 500, 0],{{h, 1}, 0, 20}, {op, 1, 0}, {{N, 4}, 1, 16, 1}, {s, 1, 100, 1}, {{r, 3.5}, 0, 10}, {z, 1, 0},{{PR, 5}, 1, 5}, {C, 0, 1, 1},{t, 0, 100, 1}]P ={1.5, 1, 4, 8, 3.8, 0.75, 0, 5, 500, 0}Manipulate[CubeTrail[P[[1]],P[[2]],P[[3]],P[[4]],P[[5]],P[[6]],t,P[[8]],500,0],{t, 1, 80, 1}]
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intothecontinuum:


Mathematica code:
Rot80 = 
 Table[
  Table[
   RotationTransform[a, {1, 1, 0}, {0, 0, 0}][Tuples[{-1, 1}, 3][[v]]],
  {v, 1, 8, 1}],
{a, 0, 2 Pi,  Pi/80}]

Edge := {1, 2, 4, 3, 7, 8, 6, 5, 1, 3, 4, 8, 7, 5, 6, 2}

CubeTrail[h_, op_, N_, s_, r_, z_, t_, PR_, IS_, C_] :=
 Graphics[
  Table[
   Scale[
    Translate[
     {AbsoluteThickness[h], Opacity[op], 
      If[C == 1, Black, White],
      Line[
       Table[
        {Rot80[[1 + Mod[t, 80]]][[Edge[[e]]]][[1]],
         Rot80[[1 + Mod[t, 80]]][[Edge[[e]]]][[2]]},
        {e, 1, 16, 1}]]},
     r{Cos[2 Pi*(n*t/80 + k)/N], Sin[2 Pi*(n*t/80 + k)/N]}],
    z^n, r{Cos[2 Pi*(n*t/80 + k)/N], Sin[2 Pi*(n*t/80 + k)/N]}],
   {k, 1, N, 1},
   {n, 1, s, 1}],
  PlotRange -> PR, ImageSize -> 500, 
  Background -> If[C == 0, Black, White]]

Manipulate[P = {h, op, N, s, r, z, t, PR, IS, C};
 CubeTrail[h, op, N, s, r, z, t, PR, 500, 0],
{{h, 1}, 0, 20}, {op, 1, 0}, 
{{N, 4}, 1, 16, 1}, {s, 1, 100, 1}, 
{{r, 3.5}, 0, 10}, {z, 1, 0},
{{PR, 5}, 1, 5}, {C, 0, 1, 1},
{t, 0, 100, 1}]

P ={1.5, 1, 4, 8, 3.8, 0.75, 0, 5, 500, 0}

Manipulate[
CubeTrail[P[[1]],P[[2]],P[[3]],P[[4]],P[[5]],P[[6]],t,P[[8]],500,0],
{t, 1, 80, 1}]
approachingsignificance: jtotheizzoe: The Beautiful Blackboards of Quantum Physics Labs Alejandro Guijarro visited the world’s finest quantum physics labs to record their half-erased blackboards. In an era where science is increasingly all-digital, it’s a striking reminder that science is still an active, hands-on process, a process here captured in layers of smeared chalk.  Visit The Atlantic for more. Ah, education. 
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approachingsignificance: jtotheizzoe: The Beautiful Blackboards of Quantum Physics Labs Alejandro Guijarro visited the world’s finest quantum physics labs to record their half-erased blackboards. In an era where science is increasingly all-digital, it’s a striking reminder that science is still an active, hands-on process, a process here captured in layers of smeared chalk.  Visit The Atlantic for more. Ah, education. 
Zoom Info
approachingsignificance: jtotheizzoe: The Beautiful Blackboards of Quantum Physics Labs Alejandro Guijarro visited the world’s finest quantum physics labs to record their half-erased blackboards. In an era where science is increasingly all-digital, it’s a striking reminder that science is still an active, hands-on process, a process here captured in layers of smeared chalk.  Visit The Atlantic for more. Ah, education. 
Zoom Info

approachingsignificance:

jtotheizzoe:

The Beautiful Blackboards of Quantum Physics Labs

Alejandro Guijarro visited the world’s finest quantum physics labs to record their half-erased blackboards. In an era where science is increasingly all-digital, it’s a striking reminder that science is still an active, hands-on process, a process here captured in layers of smeared chalk. 

Visit The Atlantic for more.

Ah, education. 

Source: jtotheizzoe

proofmathisbeautiful: Because it’s that time of year again!! Also…this is a reblog of one of my very first posts on Proof! :) The Von Koch snowflake! The Von Koch snowflake is a fractal which is constructed from an equilateral triangle as follows: 1) remove the middle third of each side, 2) build a new equilateral triangle on each of the resulting gaps, 3) repeat steps 1 and 2 for the new object. If you keep going indefinitely, you end up with the fractal shown on the right. The outline of the snowflake is incredibly crinkly. In fact, it does not contain any straight line pieces at all: the middle third of any piece of straight line has been replaced by two sides of a triangle, creating a spike. Mathematicians measure the crinkliness of a fractal by the fractal dimension, a generalisation of our ordinary notion of dimension. The outline of our snowflake is too crinkly to be one-dimensional. On the other hand, it clearly is not two-dimensional either, since it contains no area. In this case, the dimension lies between 1 and 2, in fact it is equal to log(4)/log(3) = 1.2619. (via proofmathisbeautiful)
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proofmathisbeautiful:

Because it’s that time of year again!!

Also…this is a reblog of one of my very first posts on Proof! :)

The Von Koch snowflake!

The Von Koch snowflake is a fractal which is constructed from an equilateral triangle as follows:

1) remove the middle third of each side,
2) build a new equilateral triangle on each of the resulting gaps,
3) repeat steps 1 and 2 for the new object.

If you keep going indefinitely, you end up with the fractal shown on the right.

The outline of the snowflake is incredibly crinkly. In fact, it does not contain any straight line pieces at all: the middle third of any piece of straight line has been replaced by two sides of a triangle, creating a spike. Mathematicians measure the crinkliness of a fractal by the fractal dimension, a generalisation of our ordinary notion of dimension. The outline of our snowflake is too crinkly to be one-dimensional. On the other hand, it clearly is not two-dimensional either, since it contains no area. In this case, the dimension lies between 1 and 2, in fact it is equal to log(4)/log(3) = 1.2619.

(via proofmathisbeautiful)