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}}]
Filed under: #GIF  #Mathematica  #C8  #circles  #GCG

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}}]
Filed under: #GIF  #Mathematica  #C8  #circles  #GCG

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]
Filed under: #C8  #GIF  #Mathematica  #circles

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}}]