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Another interesting dynamic solitons-and-worms pattern
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@danwills
danwills committed Aug 9, 2015
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271 changes: 271 additions & 0 deletions Patterns/Experiments/DanWills/grayscott-historyWaveDC_dualPhaseSolitonWormFlow.vti
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<description>
A gray-scott reaction-diffusion system is simulated in the a and b reagents, with two coupled simpler systems in c,d,e.
The c reagent implements a diffuse kind of &apos;history&apos; of the other reagents (ie so that gliders can leave a &apos;trail&apos;).
The d and e reagents implement the wave equation, with additional damping and shaping controls, which is fed by the other reagents (for example gliders can leave a rippley &apos;wake&apos; behind them).
The extra reagents can feed back into the gray-scott ones, and also control the gray-scott parameters (including diffusion).
Implemented by Dan Wills ([email protected]) based on existing work in the Ready codebase.

This example starts as flowing maze-like growth which *usually* (not always) decays forming a flowing field of worms and solitons. When conditions are right, they switch back to this 'elevated' form of growth, that is both stronger growing and generally more maze-forming. The dynamic behaviour switching has an interesting long-term chaotic effect on the underlying behaviour, which would otherwise tend to end in a constant state or loop.

There are very rare initial states that end up with the system stuck in the 'elevated' state, and it may stay that way for some time. So, if it looks flowing fingerprints and no dots for ages, you might need to generate a new initial state.
</description>
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<param name="timestep">
1
</param>
<param name="D_a">
0.2
</param>
<param name="D_b">
0.1
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<param name="k">
0.059
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<param name="F">
0.09
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1
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<param name="b_pow">
2
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0
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0.0152
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5e-05
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0.083
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1.0059
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2
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0
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2
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0
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0
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0.001
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-0.0009
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5e-05
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0.98
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1.005
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0
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0.019
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delta_a = (D_a + c*c_to_Da + (d-wave_DC_value)*wave_to_Da) * laplacian_a - pow(a,(float4)a_pow)*pow(b,(float4)b_pow) + (F + c_to_F*c + (d-wave_DC_value)*wave_to_F)*(1.0f-a) + c*c_to_a + (d-wave_DC_value)*wave_to_a;
delta_b = (D_b + c*c_to_Db + (d-wave_DC_value)*wave_to_Db) * laplacian_b + pow(a,(float4)a_pow)*pow(b,(float4)b_pow) - ((F + c_to_F*c + (d-wave_DC_value)*wave_to_F)+(k + c*c_to_k + (d-wave_DC_value)*wave_to_k))*b + c*c_to_b + (d-wave_DC_value)*wave_to_b;
delta_c = -c*c_damp + a*a_to_c + b*b_to_c + (d-wave_DC_value)*wave_to_c + D_c * laplacian_c;
c = clamp( pow( (float4)( fabs(c)/c_pow_norm ), (float4)c_pow )*c_pow_norm, c_clamp_min, c_clamp_max );
d = wave_DC_value + clamp( sign(d-wave_DC_value) * pow( (float4)( fabs(d-wave_DC_value) * wave_damp), (float4)wave_power ) + a * a_to_wave + b * b_to_wave + c * c_to_wave, -wave_clamp, wave_clamp);
delta_e = (laplacian_d) * wave_diffusion;
delta_d = e + delta_e;
</formula>

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