diff --git a/.gitignore b/.gitignore index 4b29612..a078c12 100644 --- a/.gitignore +++ b/.gitignore @@ -3,4 +3,6 @@ venv/ .vscode simulation_claudius.py OLD* -.DS_Store \ No newline at end of file +.DS_Store +*.backup +*.dat diff --git a/extinction_time.py b/extinction_time.py index 7ef3191..1f9015e 100644 --- a/extinction_time.py +++ b/extinction_time.py @@ -5,6 +5,7 @@ BASE_PATH = "./data/dormant-life/extinction-time" +os.makedirs(BASE_PATH, exist_ok=True) def find_extinction_time(ca: CellularAutomaton, t_max: int, diff --git a/img/birth-rate.png b/img/birth-rate.png new file mode 100644 index 0000000..f07e2cd Binary files /dev/null and b/img/birth-rate.png differ diff --git a/img/extinction-times.png b/img/extinction-times.png new file mode 100644 index 0000000..1f11273 Binary files /dev/null and b/img/extinction-times.png differ diff --git a/img/finite-size-effects.png b/img/finite-size-effects.png new file mode 100644 index 0000000..cf1179c Binary files /dev/null and b/img/finite-size-effects.png differ diff --git a/lifetime_distribution.py b/lifetime_distribution.py new file mode 100644 index 0000000..4d2781e --- /dev/null +++ b/lifetime_distribution.py @@ -0,0 +1,114 @@ +import sys, os +import numpy as np +from collections import Counter +from gol import CellularAutomaton, DormantLife +from gol import ALIVE, DEAD, DORM +from util import random_init_grid +import matplotlib.pyplot as plt + + +def lifetime_distribution(state: int, dl: DormantLife, t_max: int, t_trans: int, + ignore_transient_dynamics: bool = True) -> Counter: + """ + Generate the lifetime distribution for a given state. The given DormantLife + is stepped until t_max (skipping the transient time t_trans) and the + distibution how long any cell in the grid stayed in the state state before + transitioning is returned as a counter. Optionally, ignore cells that + transition to state within the transient time. + """ + lifetime_grid = np.zeros((dl.N, dl.N), dtype=np.intc) + dl.step_until(t_trans) + # Mask to exclude cells that are state from the get-go + if ignore_transient_dynamics: + trans_mask = dl.grid != state + else: + trans_mask = np.ones((dl.N, dl.N), dtype=np.bool_) + data = Counter() # initialize distribution + while dl.t <= t_max: + old_grid = dl.grid.copy() + new_grid = dl.step() + # Cells that are *still* in state add to lifetime grid + lifetime_grid += (trans_mask & + ((old_grid == state) & (new_grid == state))) + # Add lifetimes of cells that left state and reset lifetime grid + _mask = (trans_mask & + ((old_grid == state) & (new_grid != state))) + data.update(lifetime_grid[_mask]) + lifetime_grid[_mask] = 0 + # Update transient mask: set mask values to true for cells initially in + # state that left state. + trans_mask |= (np.logical_not(trans_mask) & (new_grid != state)) # FIXME + return data + + +def tau_distribution(dl: DormantLife, t_max: int, t_trans: int, + ignore_transient_dynamics: bool = True) -> Counter: + tau_grid = np.zeros((dl.N, dl.N), dtype=np.intc) + dl.step_until(t_trans) + if ignore_transient_dynamics: + trans_mask = dl.grid != DORM + else: + trans_mask = np.ones((dl.N, dl.N), dtype=np.bool_) + data = Counter() + while dl.t <= t_max: + old_grid = dl.grid.copy() + new_grid = dl.step() + # Count tau + tau_grid += (trans_mask & ((old_grid == DORM) & (new_grid == DORM))) + # Update distribution + data.update(tau_grid[(trans_mask & (new_grid == DORM))]) + # Reset tau grid + # NOTE: Could also add trans_mask & in front, but since tau grid is not updated for cells that are excluded through trans_mask it does not make a difference + tau_grid[(old_grid == DORM) & (new_grid != DORM)] = 0 + # Update trans_mask + trans_mask |= (np.logical_not(trans_mask) & (new_grid != DORM)) + return data + + +if __name__ == "__main__": + # # CHANGE N + # t_max = 10_000 + # fig,(ax, axx)=plt.subplots(figsize=(3*7.2, 3*3.2), ncols=2) + # alpha = .4 + # for N in [30, 300]: + # init_grid = random_init_grid(N, seed=100) + # dl = DormantLife(init_grid, alpha, seed=100) + # distr = lifetime_distribution(DORM, dl, t_max, 150, ignore_transient_dynamics=1) + # ax.scatter(distr.keys(), distr.values(), label=N) + # dl = DormantLife(init_grid, alpha, seed=100) + # axx.plot(dl.dorm_count_time_series(t_max)) + # # ax.set_xscale("log") + # ax.set_yscale("log") + # ax.legend() + # axx.legend() + + + # # CHANGE ALPHA + # t_max = 10_000 + # fig,ax=plt.subplots(ncols=2) + # for alpha in [1, .1]: + # init_grid = random_init_grid(100, seed=100) + # dl = DormantLife(init_grid, alpha, seed=100) + # distr = lifetime_distribution(DORM, dl, t_max, 150, ignore_transient_dynamics=1) + # ax[0].scatter(distr.keys(), distr.values(), label=alpha) + # dl = DormantLife(init_grid, alpha, seed=100) + # ax[1].plot(dl.dorm_count_time_series(t_max)) + # print(sum(list(distr.values()))) + # # ax[0].set_xscale("log") + # ax[0].set_yscale("log") + # ax[0].legend() + # ax[1].legend() + + + # TAU DISTRIBUTION + t_max, t_trans = 10_000, 200 + fig, ax = plt.subplots() + ax.set(yscale="log") + for alpha in [1, .8, .5, .2]: + init_grid = random_init_grid(100, seed=100) + dl = DormantLife(init_grid, alpha, seed=100) + distr = tau_distribution(dl, t_max, t_trans) + vals, counts = np.fromiter(distr.keys(), dtype=np.intc), np.fromiter(distr.values(), dtype=np.intc) + ax.scatter(vals, counts/(t_max-t_trans), label=alpha) + ax.legend() + plt.show() diff --git a/paper.mplstyle b/paper.mplstyle index 8721189..3447ebb 100644 --- a/paper.mplstyle +++ b/paper.mplstyle @@ -35,7 +35,7 @@ ytick.right : True # Set line widths axes.linewidth : 0.5 grid.linewidth : 0.5 -lines.linewidth : 1. +lines.linewidth : 2. # Remove legend frame legend.frameon : False diff --git a/plots.ipynb b/plots.ipynb index cebe0d1..0b7cc6d 100644 --- a/plots.ipynb +++ b/plots.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 183, "metadata": {}, "outputs": [], "source": [ @@ -12,7 +12,338 @@ "import matplotlib as mpl\n", "plt.style.use(\"./paper.mplstyle\")\n", "from scipy.optimize import curve_fit\n", - "from gol import DormantLife" + "from gol import DormantLife\n", + "from gol import ALIVE, DORM, DEAD\n", + "from util import random_init_grid" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Lifetime Distribution" + ] + }, + { + "cell_type": "code", + "execution_count": 122, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1838.58435205 108.33297486]\n", + "[497.55598533 106.09091529]\n" + ] + }, + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from collections import Counter\n", + "from lifetime_distribution import lifetime_distribution\n", + "\n", + "alpha = .2\n", + "t_max, t_trans = 10_000, 200\n", + "\n", + "for N, t_divide in zip([100, 50], [180, 130]):\n", + " fig, (axl, axr) = plt.subplots(figsize=(7.3, 3.3), ncols=2, sharey=1)\n", + " fig.subplots_adjust(wspace=0)\n", + " axl.set(\n", + " xscale=\"log\",\n", + " yscale=\"log\",\n", + " xlim=(1,t_divide)\n", + " )\n", + " axr.set(\n", + " yscale=\"log\",\n", + " xlim=(t_divide,1500),\n", + " ylim=(1, 10**6)\n", + " )\n", + " dl = DormantLife(random_init_grid(N, seed=100), alpha=alpha)\n", + " distr: Counter = lifetime_distribution(DORM, dl, t_max, t_trans)\n", + " vals, counts = np.fromiter(distr.keys(), np.intc), np.fromiter(distr.values(), np.intc)\n", + "\n", + " axl.scatter(vals, counts, alpha=.1)\n", + " # Fit\n", + " fit_func = lambda x, c, gamma: c*x**(-gamma)\n", + " _l_mask = ((vals20))\n", + " _l_popt, _ = curve_fit(fit_func, vals[_l_mask], counts[_l_mask], p0=(5000, 1))\n", + " _l_x = np.linspace(1, t_divide)\n", + " axl.plot(_l_x, fit_func(_l_x, *_l_popt), label=r\"$%f\\cdot t^{-%f}$\"%tuple(_l_popt))\n", + "\n", + " axr.scatter(vals, counts, alpha=.1)\n", + " # Fit\n", + " fit_func = lambda x, c, T: c*np.exp(-x/T)\n", + " _r_mask = (vals>t_divide)\n", + " _r_popt, _ = curve_fit(fit_func, vals[_r_mask], counts[_r_mask], p0=(5000, 60))\n", + " print(_r_popt)\n", + " _r_x = np.linspace(t_divide, 1500)\n", + " axr.plot(_r_x, fit_func(_r_x, *_r_popt), label=r\"$%f\\cdot\\mathrm{e}^{-t/%f}$\"%tuple(_r_popt))\n", + " axr.legend()\n", + " axl.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 153, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 153, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "N = 100; t_max = 10_000; t_trans = 200\n", + "fig, (ax, axx) = plt.subplots(figsize=(7.2, 3.2), ncols=2)\n", + "ax.set(yscale=\"log\")\n", + "axx.set(yscale=\"log\")\n", + "for alpha in [0.8, 0.5, 0.3]:\n", + " dl = DormantLife(random_init_grid(N, seed=100), alpha=alpha)\n", + " distr: Counter = lifetime_distribution(DORM, dl, t_max, t_trans)\n", + " vals, counts = np.fromiter(distr.keys(), np.intc), np.fromiter(distr.values(), np.intc)\n", + " ax.scatter(vals, counts, label=r\"$\\alpha = %.1f$\"%alpha)\n", + " axx.scatter(vals[int(len(vals)/3):], counts[int(len(vals)/3):])\n", + "ax.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 160, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.1 [145.56340308 411.24106678]\n", + "0.1310344827586207 [341.1655178 244.98000707]\n", + "0.16206896551724137 [772.83063638 163.57231541]\n", + "0.19310344827586207 [935.300849 141.19623967]\n", + "0.22413793103448276 [1276.19110033 118.53448892]\n", + "0.25517241379310346 [2460.83159351 86.88174207]\n", + "0.28620689655172415 [2932.76447699 74.44997586]\n", + "0.3172413793103448 [3086.63039824 68.9018961 ]\n", + "0.34827586206896555 [5449.9816448 51.64401127]\n", + "0.3793103448275862 [5750.22019571 47.93053036]\n", + "0.41034482758620694 [7925.34794092 40.51720244]\n", + "0.4413793103448276 [8586.35864892 37.35461856]\n", + "0.4724137931034482 [10755.44665395 32.48321953]\n", + "0.503448275862069 [12788.0884478 28.90605683]\n", + "0.5344827586206896 [16804.22824963 24.87671947]\n", + "0.5655172413793104 [14278.22247171 24.25192186]\n", + "0.596551724137931 [17398.00905332 21.24972768]\n", + "0.6275862068965516 [1494.74052319 1.86233503]\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/daniel/dev/phd/game-of-life-dormancy/venv/lib/python3.12/site-packages/scipy/optimize/_minpack_py.py:1010: OptimizeWarning: Covariance of the parameters could not be estimated\n", + " warnings.warn('Covariance of the parameters could not be estimated',\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.6586206896551724 [2.00116502e+04 1.80430417e+01]\n", + "0.689655172413793 [2.60909443e+04 1.56665516e+01]\n", + "0.7206896551724138 [2.35404386e+04 1.49389088e+01]\n", + "0.7517241379310344 [3.29819420e+04 1.27284109e+01]\n", + "0.7827586206896552 [2.73891993e+04 1.24640400e+01]\n", + "0.8137931034482758 [3.79331987e+04 1.07130537e+01]\n", + "0.8448275862068965 [3.31562430e+04 1.01832371e+01]\n", + "0.8758620689655172 [3.48894516e+04 9.16757811e+00]\n", + "0.9068965517241379 [3.13007970e+04 8.44358079e+00]\n", + "0.9379310344827586 [4.67221058e+04 6.72489365e+00]\n", + "0.9689655172413792 [6.95155881e+04 5.40208433e+00]\n", + "1.0 [1.29560915e+05 4.23901250e+00]\n" + ] + } + ], + "source": [ + "# Timescale over alpha\n", + "fit_func = lambda x, c, T: c*np.exp(-x/T)\n", + "N = 100; t_max = 10_000; t_trans = 200\n", + "alphas = np.linspace(0.1, 1, 30)\n", + "data = []\n", + "for alpha in alphas:\n", + " dl = DormantLife(random_init_grid(N), alpha=alpha)\n", + " distr: Counter = lifetime_distribution(DORM, dl, t_max, t_trans)\n", + " vals, counts = np.fromiter(distr.keys(), np.intc), np.fromiter(distr.values(), np.intc)\n", + " popt, _ = curve_fit(fit_func, vals[int(len(vals)/3):], counts[int(len(vals)/3):], p0=(1000, 100))\n", + " print(alpha, popt, flush=True)\n", + " data.append(popt[1])" + ] + }, + { + "cell_type": "code", + "execution_count": 164, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 164, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.set(yscale=\"log\", xscale=\"log\", xlabel=r\"$\\alpha$\", ylabel=r\"Asymt. Timescale $T$\")\n", + "ax.plot(alphas, data)\n", + "fit_func = lambda x, c, gamma: c*x**(-gamma)\n", + "popt, _ = curve_fit(fit_func, alphas, data)\n", + "ax.plot(alphas, fit_func(alphas, *popt), label=r\"$%f\\cdot \\alpha^{-%f}$\"%tuple(popt))\n", + "ax.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 266, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/var/folders/6p/pg8nb3s56dldh08p9t61yss40000gn/T/ipykernel_56423/2809239077.py:6: RuntimeWarning: divide by zero encountered in power\n", + " fit_func = lambda x, c, gamma: c*x**(-gamma)\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 266, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "alphas = np.loadtxt(\"data/dormant-life/time-series/grid-size-100/alpha-range.dat\")\n", + "p_L_of_alpha = np.array(avgs_t_max_100)/(100*100)\n", + "P_3_of_alpha = (p_L_of_alpha)**3 * (1-p_L_of_alpha)**5\n", + "fig, ax = plt.subplots()\n", + "ax.set(xscale=\"log\", yscale=\"log\", xlabel=r\"$\\alpha$\", ylabel=r\"Asymt. Timescale $T$\", title=\"Mean field also shows power law\")\n", + "fit_func = lambda x, c, gamma: c*x**(-gamma)\n", + "popt, _ = curve_fit(fit_func, alphas[alphas>0.1], -1/np.log(1-P_3_of_alpha[alphas>0.1]))\n", + "ax.plot(alphas, fit_func(alphas, *popt), label=r\"$%f\\cdot \\alpha^{-%f}$\"%tuple(popt))\n", + "ax.scatter(alphas, -1/np.log(1-P_3_of_alpha))\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Mean Field Model" + ] + }, + { + "cell_type": "code", + "execution_count": 275, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 275, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def compute_Q_tau(p_L, alpha, tau_max):\n", + " P_1 = p_L * (1 - p_L)**7\n", + " P_2 = p_L**2 * (1 - p_L)**6\n", + " P_3 = p_L**3 * (1 - p_L)**5\n", + " Q_tau = [p_L*P_1]\n", + " for tau in range(1, tau_max):\n", + " Q_tau.append(Q_tau[-1] * (1 - alpha**tau * P_2 - P_3))\n", + " return Q_tau\n", + "\n", + "alpha = 0.755\n", + "p_L = np.mean(load_time_series_data(100, alpha)[:100, 200:t_max])/(100**2)\n", + "fig, ax = plt.subplots()\n", + "ax.set(yscale=\"log\")\n", + "ax.plot(range(1500), compute_Q_tau(p_L, alpha, 1500))" ] }, { @@ -24,7 +355,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 185, "metadata": {}, "outputs": [], "source": [ @@ -79,7 +410,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 227, "metadata": {}, "outputs": [ { @@ -93,38 +424,17 @@ }, { "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", 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", 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" } ], "source": [ "fig, (axl, axr) = plt.subplots(1, 2, figsize=(7.2, 3.2))\n", - "fig, ax = plt.subplots()\n", "### LEFT ###\n", "axl.set(xlabel=r\"$T_\\mathrm{extinct} / \\langle T_\\mathrm{extinct} \\rangle$\",\n", " title=\"(a)\",\n", @@ -155,11 +465,15 @@ "### RIGHT ###\n", "axr.set(xlabel=r\"$\\alpha$\",\n", " ylabel=r\"$\\langle T_\\mathrm{extinct} \\rangle$ $\\left[\\times 10^3\\right]$\",\n", - " title=\"(b)\")\n", + " title=\"(b)\",\n", + " ylim=(-1, 36),\n", + " # yscale=\"log\"\n", + ")\n", "alphas = np.loadtxt(\"./data/dormant-life/extinction-time/alpha-range.dat\")\n", "# Data above alpha = 0.4 numerically biased. Extinction times too long.\n", "alphas = alphas[alphas<0.4]\n", "extinction_times = np.array([np.mean(load_extinction_time_data(alpha)) for alpha in alphas])/1000\n", + "# axr.plot(-1/np.log(alphas[1:]), extinction_times[1:], color=\"gray\")\n", "axr.plot(alphas, extinction_times, color=\"gray\")\n", "# Draw marker for Game of Life\n", "axr.annotate(\"Game of Life\", (0, extinction_times[0]), xytext=(0., 10),\n", @@ -169,8 +483,12 @@ "axr.scatter(x=0, y=extinction_times[0], c=\"tab:blue\", zorder=10)\n", "# Mark alphas from axl\n", "axr.scatter(x=0.2, y=extinction_times[15]-0.1, c=\"tab:cyan\", zorder=10, alpha=0.5)\n", + "axr.vlines(0.2, -1, extinction_times[15]-0.6, colors=\"tab:cyan\", linestyles=\"dashed\")\n", "axr.scatter(x=0.3, y=extinction_times[22]-0.15, c=\"tab:purple\", zorder=10, alpha=0.5)\n", - "axr.scatter(x=0.35, y=extinction_times[25]+2.3, c=\"tab:red\", zorder=10, alpha=0.5)" + "axr.vlines(0.3, -1, extinction_times[22]-0.9, colors=\"tab:purple\", linestyles=\"dashed\")\n", + "axr.scatter(x=0.35, y=extinction_times[25]+2.3, c=\"tab:red\", zorder=10, alpha=0.5)\n", + "axr.vlines(0.35, -1, extinction_times[25]+1.5, colors=\"tab:red\", linestyles=\"dashed\")\n", + "fig.savefig(\"img/extinction-times.png\", bbox_inches=\"tight\")" ] }, { @@ -182,7 +500,7 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 187, "metadata": {}, "outputs": [], "source": [ @@ -197,6 +515,109 @@ " return np.mean(time_series_data, axis=0)" ] }, + { + "cell_type": "code", + "execution_count": 188, + "metadata": {}, + "outputs": [], + "source": [ + "t_max = 10000\n", + "avgs_t_max_20 = []\n", + "avgs_t_max_30 = []\n", + "avgs_t_max_100 = []\n", + "alphas = np.loadtxt(\"data/dormant-life/time-series/grid-size-100/alpha-range.dat\")\n", + "for alpha in alphas:\n", + " data_20 = load_time_series_data(20, alpha)\n", + " data_30 = load_time_series_data(30, alpha)\n", + " data_100 = load_time_series_data(100, alpha)\n", + " avgs_t_max_20.append(np.mean(data_20[:100, 200:t_max]))\n", + " avgs_t_max_30.append(np.mean(data_30[:100, 200:t_max]))\n", + " avgs_t_max_100.append(np.mean(data_100[:100, 200:t_max]))" + ] + }, + { + "cell_type": "code", + "execution_count": 228, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "alphas = np.loadtxt(\"data/dormant-life/time-series/grid-size-100/alpha-range.dat\")\n", + "ax.set(xlabel=r\"$\\alpha$\", ylabel=r\"$\\langle\\rho_\\mathrm{ALIVE}\\rangle$\")\n", + "ax.plot(alphas, np.array(avgs_t_max_20)/(20*20), label=r\"$N = 20$\", linestyle=\"-.\", c=\"gray\")\n", + "ax.plot(alphas, np.array(avgs_t_max_30)/(30*30), label=r\"$N = 30$\", linestyle=\"--\", c=\"gray\")\n", + "ax.plot(alphas, np.array(avgs_t_max_100)/(100*100), label=r\"$N=100$\", linestyle=\"-\", c=\"gray\")\n", + "ax.annotate(\"Game of Life\", (0, (np.array(avgs_t_max_100)/(100*100))[0]), xytext=(.05, .1),\n", + " arrowprops={\"arrowstyle\":\"->\", \"relpos\":(0.1, 0.1),\n", + " \"color\":\"tab:blue\", \"shrinkB\":5},\n", + " c=\"tab:blue\", backgroundcolor=\"w\", bbox={\"ec\": \"tab:blue\", \"fc\": \"white\"}) # edge color and face color\n", + "ax.scatter(x=0, y=(np.array(avgs_t_max_100)/(100*100))[0], c=\"tab:blue\", zorder=10)\n", + "ax.annotate(\"Dormant Life\", (1, (np.array(avgs_t_max_100)/(100*100))[-1]), xytext=(.6, .17),\n", + " arrowprops={\"arrowstyle\":\"->\", \"relpos\":(0.65, 0.5),\n", + " \"color\":\"tab:orange\", \"shrinkB\":5},\n", + " c=\"tab:orange\")\n", + "ax.scatter(x=1, y=(np.array(avgs_t_max_100)/(100*100))[-1], c=\"tab:orange\", zorder=10)\n", + "ax.legend()\n", + "fig.savefig(\"img/finite-size-effects.png\", bbox_inches=\"tight\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Transitions" + ] + }, + { + "cell_type": "code", + "execution_count": 229, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "base_path = \"data/dormant-life/state-transitions/to-alive-transitions\"\n", + "alphas = np.loadtxt(os.path.join(base_path, \"alpha-range.dat\"))\n", + "transitions = [np.mean(np.loadtxt(os.path.join(base_path, f\"alpha-{str(alpha)[0]}p{str(alpha)[2:]}.dat\"))) for alpha in alphas]\n", + "\n", + "birth_rate = transitions/(np.array(avgs_t_max_100))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set(xlabel=r\"$\\alpha$\", ylabel=r\"Birth Rate\")\n", + "ax.plot(alphas, birth_rate, c=\"gray\")\n", + "ax.annotate(\"Game of Life\", (0, birth_rate[0]), xytext=(.15, .25),\n", + " arrowprops={\"arrowstyle\":\"->\", \"relpos\":(0.5, 0.5),\n", + " \"color\":\"tab:blue\", \"shrinkB\":10},\n", + " c=\"tab:blue\") # edge color and face color\n", + "ax.scatter(x=0, y=birth_rate[0], c=\"tab:blue\", zorder=10)\n", + "ax.annotate(\"Dormant Life\", (1, birth_rate[-1]), xytext=(.55, .4),\n", + " arrowprops={\"arrowstyle\":\"->\", \"relpos\":(0.65, 0.5),\n", + " \"color\":\"tab:orange\", \"shrinkB\":5},\n", + " c=\"tab:orange\")\n", + "ax.scatter(x=1, y=birth_rate[-1], c=\"tab:orange\", zorder=10)\n", + "fig.savefig(\"img/birth-rate.png\", bbox_inches=\"tight\")" + ] + }, { "cell_type": "markdown", "metadata": {}, diff --git a/simulation.py b/simulation.py index ee476da..139e89f 100644 --- a/simulation.py +++ b/simulation.py @@ -3,16 +3,18 @@ import numpy as np from matplotlib.colors import ListedColormap, BoundaryNorm from gol import GameOfLife, DormantLife, DEAD, ALIVE, DORM +from lifetime_distribution import lifetime_distribution if __name__ == "__main__": - init_grid = np.random.choice([0, 1], p=[0.80, 0.20], size=[30, 30]) - # init_grid = np.array([ - # [0, 0, 0], - # [1, 1, 0], - # [1, 1, 0] - # ]) + # init_grid = np.random.choice([0, 1], p=[0.80, 0.20], size=[30, 30]) + init_grid = np.array([ + [0, 0, 1, 0], + [0, 1, 0, 0], + [1, 0, 0, 0], + [1, 0, 0, 0] + ]) gol = GameOfLife(init_grid) - dl = DormantLife(init_grid, alpha=1) + dl = DormantLife(init_grid, alpha=.3) colors = ["white", "tab:blue", "lightblue"] cmap = ListedColormap(colors) fig, ax = plt.subplots(figsize=(7.2, 3.2), ncols=2) @@ -21,11 +23,12 @@ mat_gol = ax[0].matshow(gol.grid, cmap=cmap, vmin=0, vmax=2) mat_dl = ax[1].matshow(dl.grid, cmap=cmap, vmin=0, vmax=2) def update(frame): + print(dl.p_grid) mat_gol.set_data(gol.grid) mat_dl.set_data(dl.grid) ax[0].set(title=r"Game of Life: $N_\text{alive} = %d$"%gol.alive_count) ax[1].set(title=r"Dormant Life: $N_\text{alive} = %d$"%dl.alive_count) gol.step() dl.step() - ani = animation.FuncAnimation(fig, update, interval=10, save_count=100) + ani = animation.FuncAnimation(fig, update, interval=1000, save_count=100) plt.show() diff --git a/state_transitions.py b/state_transitions.py index 95ac3de..8a57cea 100644 --- a/state_transitions.py +++ b/state_transitions.py @@ -8,6 +8,7 @@ BASE_PATH = "data/dormant-life/state-transitions/to-alive-transitions" +os.makedirs(BASE_PATH, exist_ok=True) def count_transitions(pre_grid: np.ndarray, post_grid: np.ndarray, diff --git a/tests.py b/tests.py index 4cddf18..86ecfbf 100644 --- a/tests.py +++ b/tests.py @@ -1,7 +1,7 @@ import unittest import numpy as np from gol import GameOfLife, DormantLife, ALIVE, DORM, DEAD - +from lifetime_distribution import lifetime_distribution class TestDormantLife(unittest.TestCase): def test_ALIVE_DORM_conversion(self): @@ -85,18 +85,42 @@ def test_stochastic_update(self): ]) np.testing.assert_array_equal(grid_step, res) - def test_transitions(self): + # def test_transitions(self): + # test_grid = np.array([ + # [DEAD, ALIVE, DORM], + # [DEAD, ALIVE, DORM], + # [DEAD, DEAD, DEAD] + # ]) + # gol = DormantLife(test_grid) + # grid_step = gol.step() + # self.assertEqual(gol.transitions_from(test_grid, ALIVE, DORM), 2) + # self.assertEqual(gol.transitions_from(test_grid, DORM, ALIVE), 2) + # self.assertEqual(gol.transitions_from(test_grid, ALIVE, DEAD), 0) + # self.assertEqual(gol.transitions_from(test_grid, DEAD, ALIVE), 0) + + +class TestLifetimeDistribution(unittest.TestCase): + def test_lifetime_measuring(self): test_grid = np.array([ - [DEAD, ALIVE, DORM], - [DEAD, ALIVE, DORM], - [DEAD, DEAD, DEAD] + [DEAD, ALIVE, DEAD], + [DEAD, ALIVE, ALIVE], + [DEAD, DEAD, DEAD] ]) - gol = DormantLife(test_grid) - grid_step = gol.step() - self.assertEqual(gol.transitions_from(test_grid, ALIVE, DORM), 2) - self.assertEqual(gol.transitions_from(test_grid, DORM, ALIVE), 2) - self.assertEqual(gol.transitions_from(test_grid, ALIVE, DEAD), 0) - self.assertEqual(gol.transitions_from(test_grid, DEAD, ALIVE), 0) + dl = DormantLife(test_grid) + self.assertDictEqual( + lifetime_distribution(ALIVE, dl, 3, 0, exclude_alive_after_trans=0), + {0: 6, 1: 3}) + + def test_exclude_alive_after_trans(self): + test_grid = np.array([ + [DEAD, ALIVE, DEAD], + [DEAD, ALIVE, ALIVE], + [DEAD, DEAD, DEAD] + ]) + dl = DormantLife(test_grid) + self.assertDictEqual( + lifetime_distribution(ALIVE, dl, 3, 0, exclude_alive_after_trans=1), + {0: 6}) if __name__ == '__main__': diff --git a/time_series.py b/time_series.py index b8ba6c1..a4b1545 100644 --- a/time_series.py +++ b/time_series.py @@ -1,11 +1,12 @@ import sys, os import numpy as np import multiprocessing -from gol import CellularAutomaton, DormantLife +from gol import DormantLife -GRID_SIZE = 100 +GRID_SIZE = 20 BASE_PATH = f"data/dormant-life/time-series/grid-size-{GRID_SIZE}" +os.makedirs(BASE_PATH, exist_ok=True) def alive_dorm_time_series(dl: DormantLife, @@ -49,8 +50,10 @@ def dormant_life_time_series(grid_size: int, def save_data(alive_data, dorm_data, alpha, header: str): fname = f"alpha-{str(alpha)[0]}p{str(alpha)[2:]}.dat" + os.makedirs(os.path.join(BASE_PATH, "alive"), exist_ok=True) np.savetxt(os.path.join(BASE_PATH, "alive", fname), (alive_data), header=header) + os.makedirs(os.path.join(BASE_PATH, "dorm"), exist_ok=True) np.savetxt(os.path.join(BASE_PATH, "dorm", fname), (dorm_data), header=header) @@ -71,7 +74,7 @@ def compute(alpha): np.savetxt(os.path.join(BASE_PATH, "alpha-range.dat"), (alphas), header="Alpha values for which data is stored.") - with multiprocessing.Pool(processes=3) as pool: + with multiprocessing.Pool(processes=4) as pool: # Use imap_unordered to apply the function to each value of alpha in # parallel and yield the results as they are ready, regardless of the # order