a perspective on mathematics, the pattern, and the abstract
Posts tagged: C8
Created using only circles subjected to constrained randomness. Every instant is a unique configuration.
Music: “Dark” by Moritz Von Oswald Trio
Mathematica code:
RR[n_, m_] := (SeedRandom[n*m]; RandomReal[])
G[t_, r_, Q_] :=
Graphics[
Table[
Table[
{RGBColor[RR[i, Q], RR[i, 2*Q], RR[i, 3*Q],
.25*Exp[-(Mod[t, 2] - .5 - RR[i, 5*Q])^2/.1]],
Disk[
RotationTransform[(k + (-1)^(i)*Mod[t, 2])*2 Pi/8]
[{r*RR[2 i, 4*Q], r*RR[2 i + 1, 4*Q]}],
(.075 + .1 RR[i, Q])*Exp[-(Mod[t, 2] - .5 - RR[i, 5*Q])^2/.1]]},
{k, 0, 7, 1}],
{i, 1, 30, 1}],
PlotRange -> 1.15, ImageSize -> 640, Background -> Black]
Manipulate[
Show[
Table[
G[.02 t + k,
If[.02 t < 2, .1 + 0.283 Sqrt[.02 t], .45 + .05 Cos[2 Pi*t/100]],
2*Ceiling[(.02 t + k)/2] + k],
{k, 0, 1, 1}]],
{t, 1567, 2000, 1}]
Mathematica code:
RR[n_, m_] := (SeedRandom[n*m]; RandomReal[])
L[t_, Q_, g_, i_] := Sum[ Exp[-(t - (RR[i, 5*Q] + j))^2/g], {j, {-1, 0, 1}}]
G[c_, F_, P_, s_, o_, g_, A_, a_, w_, t_, r_, Q_, pr_, is_] :=
Graphics[
Table[
Table[
{RGBColor[RR[i, Q], RR[i, 2*Q], RR[i, 3*Q], o + A*L[t, 5*Q, g, i]],
Disk[
RotationTransform[(k + (-1)^(i*w)*t*a)*2 Pi/F]
[{r*RR[2 i, 4*Q], r*RR[2 i + 1, 4*Q]}], s*L[t, 5*Q, g, i]]},
{k, 0, F - 1, 1}],
{i, 1, P, 1}],
PlotRange -> pr, ImageSize -> is, Background -> If[c == 0, White, Black]]
Table[
ListAnimate[
Table[
G[1, 8, 30, .12, 0, .1, .25, 1, 1, t, .5, Q, .5, 500]
{t, 0, 15/16, 1/16}],
AnimationRunning -> False],
{Q, {33, 34}}]
click through to view in higher res. (500x500)
Mathematica code:
RR[n_, m_] := (SeedRandom[n*m]; RandomReal[])
L[t_, Q_, g_, i_] := Sum[ Exp[-(t - (RR[i, 5*Q] + j))^2/g], {j, {-1, 0, 1}}]
G[c_, F_, P_, s_, o_, g_, A_, a_, w_, t_, r_, Q_, pr_, is_] :=
Graphics[
Table[
Table[
{RGBColor[RR[i, Q], RR[i, 2*Q], RR[i, 3*Q], o + A*L[t, 5*Q, g, i]],
Disk[
RotationTransform[(k + (-1)^(i*w)*t*a)*2 Pi/F]
[{r*RR[2 i, 4*Q], r*RR[2 i + 1, 4*Q]}], s*L[t, 5*Q, g, i]]},
{k, 0, F - 1, 1}],
{i, 1, P, 1}],
PlotRange -> pr, ImageSize -> is, Background -> If[c == 0, White, Black]]
Table[
ListAnimate[
Table[
G[0, 8, 20, .3, 0, .1, .25, 1, 1, t, .75, Q, 1.3, 500],
{t, 0, .96, .04}],
AnimationRunning -> False],
{Q, {1, 9, 12, 17, 18, 19}}]
Animated GIF (700x700)
Mathematica code:
R[n_] := (SeedRandom[n]; RandomReal[])
RE[n_] := (SeedRandom[n]; RandomReal[ExponentialDistribution[4]])
G[Q_, t_] :=
Graphics[
Table[
{PointSize[ .06* (Sqrt[RE[Q*2 i^2] + RE[Q*2 i + 1]^2])],
Opacity[ .5*Sum[Exp[-(t - (R[Q*i] + j))^2/.1], {j, {-1, 0, 1}}]],
Point[
Table[
RotationTransform[(k + (-1)^(i)*t)*2 Pi/8]
[{RE[Q*2 i],RE[Q*2 i +1]}],
{k, 0, 7, 1}]]},
{i, 1, 200, 1}],
PlotRange -> If[Q == 25, 1.4, 1.2], ImageSize -> 700]
Table[
ListAnimate[
Table[
G[Q,t],
{t, 0, .95, .05}],
AnimationRunning -> False],
{Q, {25, 35}}]
Mathematica code:
R[n_] := (SeedRandom[n]; RandomReal[])
RE[n_] := (SeedRandom[n]; RandomReal[ExponentialDistribution[4]])
G[Q_, t_] :=
Graphics[
Table[
{PointSize[ .06* (Sqrt[RE[Q*2 i^2] + RE[Q*2 i + 1]^2])],
Opacity[.2 + .4*Sum[Exp[-(t - (R[Q*i] + j))^2/.1], {j, {-1, 0, 1}}]],
Point[
Table[
RotationTransform[(k + (-1)^(i)*t)*2 Pi/8]
[{RE[Q*2 i],RE[Q*2 i +1]}],
{k, 0, 7, 1}]]},
{i, 1, 90, 1}],
PlotRange -> 1.5, ImageSize -> 500]
Table[
ListAnimate[
Table[
G[Q,t],
{t, 0, .95, .05}],
AnimationRunning -> False],
{Q, {4, 8, 11, 13, 15, 18 }]
Animated GIF (700x700)
- Choose 300 random points in some region of the plane over some time interval.
- For each point, create 7 copies obtained by consecutive rotations around the origin by 45ยบ.
- Let each set of 8 points decrease exponentially in opacity starting at some random time in that interval.
In the animation above the time interval loops about every 3 seconds, and there are 2400 points in total.
Mathematica code:
R[n_] := (SeedRandom[n]; RandomReal[])
Animate[
Graphics[
Table[
{PointSize[.015], Opacity[Exp[-.8 (Mod[t - 5*R[14*i], 5])]],
Point[
Table[
RotationTransform[k*2 Pi/8][{R[14*2 i], R[14*2 i + 1]}],
{k, 0, 7, 1}]]},
{i, 1, 300, 1}],
PlotRange -> 1.4, ImageSize -> 500],
{t, 0, 29/6, 1/6}, AnimationRunning ->False]
Symmetry is merely an expression of how something stands in relation to itself.
Mathematica code:
R[n_] := (SeedRandom[n]; RandomReal[])
Table[
Animate[
Graphics[
Table[
{PointSize[.03], Opacity[Exp[-.8 (Mod[t - 5*R[Q*i], 5])]],
Point[
Table[
RotationTransform[k*2 Pi/8][{R[Q*2 i], R[Q*2 i + 1]}],
{k, 0, 7, 1}]]},
{i, 1, 100, 1}],
PlotRange -> 1.33, ImageSize -> 500],
{t, 0, 29/6, 1/6}, AnimationRunning ->False],
{Q, {5, 7, 10, 14}}]
