diff --git a/bigneurallife.py b/bigneurallife.py new file mode 100644 index 0000000..a9c80af --- /dev/null +++ b/bigneurallife.py @@ -0,0 +1,178 @@ +#!/usr/bin/python +# -*- coding: utf-8 -*- + +__author__ = "Aleksey Lobanov" +__copyright__ = "Copyright 2016, Aleksey Lobanov" +__credits__ = ["Aleksey Lobanov"] +__license__ = "MIT" +__maintainer__ = "Aleksey Lobanov" +__email__ = "i@likemath.ru" + +import sys +from copy import deepcopy +from datetime import datetime +import logging + +import numpy as np + +from sklearn.cross_validation import train_test_split + +import keras +from keras.models import Sequential +from keras.layers import Dense, Dropout + +import matplotlib.pyplot as plt +import matplotlib.cm as cm +import matplotlib.patches as mpatches + + +def initLogging(): + logger = logging.getLogger() + logger.setLevel(logging.DEBUG) + + formatter = logging.Formatter('%(asctime)s - %(levelname)s - %(message)s') + fh = logging.FileHandler('neurallife.log') + fh.setLevel(logging.DEBUG) + fh.setFormatter(formatter) + logger.addHandler(fh) + ch = logging.StreamHandler() + ch.setLevel(logging.DEBUG) + ch.setFormatter(formatter) + logger.addHandler(ch) + + +def neighbors(field, i, j, fsize): + nsum = 0 + for l in range(1, 10): + x = i - 1 + (l - 1) // 3 + y = j - 1 + (l + 2) % 3 + if -1 < x < fsize and -1 < y < fsize and field[x][y] == 1: + nsum += 1 + nsum -= field[i][j] + return nsum + + +def nextGen(field, fsize): + tmp_field = deepcopy(field) + for i in range(fsize): + for j in range(fsize): + neighb = neighbors(tmp_field, i, j, fsize) + if field[i][j] == 1 and not (2 <= neighb <= 3): + field[i][j] = 0 + elif field[i][j] == 0 and neighb == 3: + field[i][j] = 1 + + +def uniqueRows(data): + uniq = np.unique(data.view(data.dtype.descr * data.shape[1])) + return uniq.view(data.dtype).reshape(-1, data.shape[1]) + + +def generateData(board_size, count=10**5): + assert(2**(board_size**2) >= count) + X = np.random.randint(2, size=(int(count*1.2),board_size*board_size)) + X = uniqueRows(X)[:count] + Y = [] + for row in X: + tmp_list = row.reshape((board_size,board_size)).tolist() + nextGen(tmp_list, board_size) + Y.append(tmp_list) + return (X, np.asarray(Y).reshape(X.shape)) + + +def loadKeras(path): + model = keras.models.model_from_json(open(path + '.json').read()) + model.load_weights(path + '.h5') + model.compile(loss='MSE', optimizer='nadam', metrics=[]) + + logging.debug("Keras model loaded from {}".format(path)) + return model + + +def saveKeras(model, path): + json_architecture = model.to_json() + json_path = path + '.json' + with open(json_path, 'w') as f: + f.write(json_architecture) + weights_path = path + '.h5' + model.save_weights(weights_path, overwrite=True) + + +def getModel(n): + nn = Sequential() + nn.add(Dense(8*n**2, input_dim=n**2, init="normal", activation="sigmoid")) + nn.add(Dense(5*n**2,init="normal", activation="sigmoid")) + nn.add(Dense(n**2,init="normal", activation="sigmoid")) + nn.compile(loss="MSE", optimizer="nadam", metrics=[]) + return nn + + +def getAccuracies(model,x_test,y_test): + preds = model.predict(x_test) + preds = np.rint(preds).astype("int") + acc_square = 1.0 * (preds == y_test).sum() / y_test.size + acc_boards = 0 + for pred, real in zip(preds, y_test): + if (pred != real).sum() == 0: + acc_boards += 1 + acc_boards = 1.0 * acc_boards / y_test.shape[0] + return (acc_square, acc_boards) + + + +META_PARAMETERS = { + 9:[409600], +} + + +if __name__ == "__main__": + initLogging() + + plt.title("Neural Life") + + plt.xscale("log") + + plt.xlabel("Train size") + plt.ylabel("Cell accuracy") + + plt_patches = [] + for meta_ind,N in enumerate(META_PARAMETERS): + points_x = [] + points_y = [] + for data_size in META_PARAMETERS[N]: + cur_time = datetime.now() + + X_train, X_test, Y_train, Y_test = train_test_split( + *generateData(N, data_size), # X and Y + test_size=0.6, + random_state=23 + ) + + train_size = X_train.shape[0] + + nn = getModel(N) + + nn.fit(X_train, Y_train, nb_epoch=40, shuffle=False, verbose=1) + + cellAcc, boardAcc = getAccuracies(nn, X_test, Y_test) + + points_x.append(train_size) + points_y.append(cellAcc) + + logging.info(("BIG model: for board {}x{} with train size={} cell accuracy is {:.5f}%, " + + "board accuracy is {:.5f}% and delta with theoretical board accuracy " + + "is {:.8f}% it takes {}").format( + N, + N, + train_size, + 100 * cellAcc, + 100 * boardAcc, + 100 * abs(boardAcc - cellAcc**(N**2)), + datetime.now() - cur_time + )) + saveKeras(nn, "models/bigmodel_{}_{}".format(N,train_size)) + plt.plot(points_x, points_y, "o", linestyle="-", color=cm.ocean(meta_ind/len(META_PARAMETERS))) + plt_patches.append(mpatches.Patch(color=cm.ocean(meta_ind/len(META_PARAMETERS)), label="N={}".format(N))) + + plt.legend(handles=plt_patches) + plt.savefig("biggraphics.svg") diff --git a/getconvolutional.py b/getconvolutional.py new file mode 100644 index 0000000..78e9337 --- /dev/null +++ b/getconvolutional.py @@ -0,0 +1,67 @@ +#!/usr/bin/python +# -*- coding: utf-8 -*- + +__author__ = "Aleksey Lobanov" +__copyright__ = "Copyright 2016, Aleksey Lobanov" +__credits__ = ["Aleksey Lobanov"] +__license__ = "MIT" +__maintainer__ = "Aleksey Lobanov" +__email__ = "i@likemath.ru" + +from datetime import datetime + +from keras.models import Sequential +from keras.layers import Dense, Dropout, Activation, Flatten +from keras.layers import Convolution2D + +import numpy as np + +from sklearn.cross_validation import train_test_split + +from neurallife import generateData, getAccuracies, saveKeras + + +def getModel(n): + nn = Sequential() + nn.add(Convolution2D(64, 3, 3, border_mode='same', input_shape=(1, n, n))) + nn.add(Activation('relu')) + nn.add(Dropout(0.25)) + nn.add(Flatten()) + nn.add(Dense(4*n**2,init="normal", activation="sigmoid")) + nn.add(Dropout(0.15)) + nn.add(Dense(n**2,init="normal", activation="sigmoid")) + nn.compile(loss="MSE", optimizer="nadam", metrics=[]) + return nn + +N = 9 # board size + +if __name__ == "__main__": + + X_train, X_test, Y_train, Y_test = train_test_split( + *generateData(N, 2*10**5), + test_size=0.5, + random_state=23 + ) + X_train = X_train.reshape((X_train.shape[0], 1, N, N)) + X_test = X_test.reshape((X_test.shape[0], 1, N, N)) + + nn = getModel(N) + + cur_time = datetime.now() + + nn.fit(X_train, Y_train, nb_epoch=20, shuffle=False, verbose=1) + + cellAcc, boardAcc = getAccuracies(nn, X_test, Y_test) + + print(("for board {}x{} with train size={} cell accuracy is {:.5f}%, " + + "board accuracy is {:.5f}% and delta with theoretical board accuracy " + + "is {:.8f}% it takes {}").format( + N, + N, + X_train.shape[0], + 100 * cellAcc, + 100 * boardAcc, + 100 * abs(boardAcc - cellAcc**(N**2)), + datetime.now() - cur_time + )) + saveKeras(nn, "models/convolutional_{}_{}".format(N, X_train.shape[0])) diff --git a/gifcreator.py b/gifcreator.py new file mode 100644 index 0000000..d007110 --- /dev/null +++ b/gifcreator.py @@ -0,0 +1,157 @@ +#!/usr/bin/python +# -*- coding: utf-8 -*- + +__author__ = "Aleksey Lobanov" +__copyright__ = "Copyright 2016, Aleksey Lobanov" +__credits__ = ["Aleksey Lobanov"] +__license__ = "MIT" +__maintainer__ = "Aleksey Lobanov" +__email__ = "i@likemath.ru" + +import sys +from copy import deepcopy + +import numpy as np + +import keras +from keras.models import Sequential +from keras.layers import Dense + +import imageio # for gifs + +from PIL import Image, ImageDraw + +from neurallife import nextGen + + +""" +# from original article +start_pos = [ + [0,0,0,0,1,0,1,0,0], + [0,1,0,0,1,0,0,1,0], + [0,1,1,0,1,1,0,1,0], + [1,0,0,1,1,0,0,0,0], + [0,1,1,1,0,1,0,1,0], + [0,0,1,0,1,0,0,0,0], + [0,0,1,1,0,0,1,0,0], + [0,1,1,0,1,1,0,0,0], + [0,0,0,0,0,0,0,0,0] +] +""" + +# about 27 original positions +start_pos = [ + [0, 0, 0, 0, 0, 0, 0, 1, 0], + [0, 0, 0, 0, 0, 0, 1, 1, 0], + [0, 0, 1, 0, 0, 1, 1, 1, 0], + [1, 0, 1, 0, 1, 0, 0, 0, 0], + [1, 0, 1, 0, 1, 1, 0, 0, 0], + [0, 1, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 1, 0, 0, 0], + [0, 0, 0, 0, 0, 1, 1, 0, 0] +] + + +""" +Code for good, long start positions: + +def getBest(max_cnt): + cur_max = 0 + cur_best = None + for i in range(max_cnt): + cur_field = np.random.randint(2, size=(9,9)).tolist() + cur_cnt = getCnt(cur_field) + if cur_cnt > cur_max: + cur_max = getCnt(cur_field, 200) + cur_best = cur_field + return (cur_best,cur_max) + + +def getCnt(pos, max_cnt=100): + cnt = 0 + ker_pred = pos + cur_pos = pos + while True: + cnt += 1 + ker_pred = nn.predict(np.asarray(ker_pred).reshape((1,1,9,9))) + ker_pred = np.rint(ker_pred).astype("int").reshape((9,9)).tolist() + + old_cur_pos = deepcopy(cur_pos) + next_gen(cur_pos, len(cur_pos)) + if np.asarray(old_cur_pos).sum() == np.asarray(cur_pos).sum(): + break + if ker_pred != cur_pos: + break + if cnt > max_cnt: + return 0 + return cnt +""" + +LINE_SIZE = 2 +SQUARE_SIZE = 18 +FRAME_COUNT = 30 +FRAME_DELAY = 0.3 # in seconds + + +def loadKeras(path): + model = keras.models.model_from_json(open(path + '.json').read()) + model.load_weights(path + '.h5') + model.compile(loss='MSE', optimizer='nadam', metrics=[ ]) + return model + + +def imageFromList(l): + global LINE_SIZE, SQUARE_SIZE + height = LINE_SIZE * (len(l) + 1) + SQUARE_SIZE * len(l) # =height + width = LINE_SIZE * (len(l[0]) + 1) + SQUARE_SIZE * len(l[0]) + tmp_img = Image.new('RGB', (width, height), (0, 0, 0)) + pil_draw = ImageDraw.Draw(tmp_img) + for y in range(len(l)): + for x in range(len(l[0])): + if l[y][x] == 0: + pil_draw.rectangle(( + x * (LINE_SIZE + SQUARE_SIZE) + LINE_SIZE, + y * (LINE_SIZE + SQUARE_SIZE) + LINE_SIZE, + (x + 1) * (LINE_SIZE + SQUARE_SIZE)-1, + (y + 1) * (LINE_SIZE + SQUARE_SIZE)-1, + ), fill=(255, 255, 255)) + return tmp_img + +N = 9 # board size + +if __name__ == '__main__': + nn = loadKeras(sys.argv[1]) + nn_frames = [] + real_frames = [] + ker_pred = cur_pos = start_pos + + for i in range(FRAME_COUNT): + #ker_pred = cur_pos + + nn_frames.append(imageFromList(ker_pred)) + ker_pred = nn.predict(np.asarray(ker_pred).reshape((1, N**2))) + ker_pred = np.rint(ker_pred).astype("int").reshape((N, N)).tolist() + + real_frames.append(imageFromList(cur_pos)) + old_pos = deepcopy(cur_pos) + nextGen(cur_pos, len(start_pos)) + + # because need some pause at end + #if cur_pos == old_pos: + # break + width, height = nn_frames[0].size + + imageio.mimsave( + 'gif_neural.gif', + [np.asarray(img.getdata()).reshape((width, height, 3)) for img in nn_frames], + fps=1/FRAME_DELAY + ) + imageio.mimsave( + 'gif_real.gif', + [np.asarray(img.getdata()).reshape((width, height, 3)) for img in real_frames], + fps=1/FRAME_DELAY + ) + + + diff --git a/graphics.gif b/graphics.gif new file mode 100644 index 0000000..7daac0c Binary files /dev/null and b/graphics.gif differ diff --git a/graphics.svg b/graphics.svg new file mode 100644 index 0000000..820b76d --- /dev/null +++ b/graphics.svg @@ -0,0 +1,2415 @@ + + + + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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diff --git a/images/gif_real.gif b/images/gif_real.gif new file mode 100644 index 0000000..4266209 Binary files /dev/null and b/images/gif_real.gif differ diff --git a/images/graphics_mini.png b/images/graphics_mini.png new file mode 100644 index 0000000..d90a1b8 Binary files /dev/null and b/images/graphics_mini.png differ diff --git a/images/graphicsboard.svg b/images/graphicsboard.svg new file mode 100644 index 0000000..70fb6da --- /dev/null +++ b/images/graphicsboard.svg @@ -0,0 +1,2350 @@ + + + + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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"sigmoid", "output_dim": 81, "bias": true, "activity_regularizer": null}}]} \ No newline at end of file diff --git a/models/convolution_8_51200.h5 b/models/convolution_8_51200.h5 new file mode 100644 index 0000000..d359fbb Binary files /dev/null and b/models/convolution_8_51200.h5 differ diff --git a/models/convolution_8_51200.json b/models/convolution_8_51200.json new file mode 100644 index 0000000..18c93b6 --- /dev/null +++ b/models/convolution_8_51200.json @@ -0,0 +1 @@ +{"config": [{"class_name": "Convolution2D", "config": {"W_regularizer": null, "nb_row": 3, "name": "convolution2d_6", "input_dtype": "float32", "b_regularizer": null, "nb_col": 3, "trainable": true, "subsample": [1, 1], "bias": true, "W_constraint": null, "border_mode": "same", "activity_regularizer": null, "b_constraint": null, "activation": "linear", "batch_input_shape": [null, 1, 8, 8], "init": "glorot_uniform", "nb_filter": 40, "dim_ordering": "th"}}, {"class_name": "Activation", "config": {"activation": "relu", 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b/neurallife.py @@ -0,0 +1,194 @@ +#!/usr/bin/python +# -*- coding: utf-8 -*- + +__author__ = "Aleksey Lobanov" +__copyright__ = "Copyright 2016, Aleksey Lobanov" +__credits__ = ["Aleksey Lobanov"] +__license__ = "MIT" +__maintainer__ = "Aleksey Lobanov" +__email__ = "i@likemath.ru" + +import sys +from copy import deepcopy +from datetime import datetime +import logging + +import numpy as np + +from sklearn.cross_validation import train_test_split + +import keras +from keras.models import Sequential +from keras.layers import Dense, Dropout + +import matplotlib.pyplot as plt +import matplotlib.cm as cm +import matplotlib.patches as mpatches + + +def initLogging(): + logger = logging.getLogger() + logger.setLevel(logging.DEBUG) + + formatter = logging.Formatter('%(asctime)s - %(levelname)s - %(message)s') + fh = logging.FileHandler('neurallife.log') + fh.setLevel(logging.DEBUG) + fh.setFormatter(formatter) + logger.addHandler(fh) + ch = logging.StreamHandler() + ch.setLevel(logging.DEBUG) + ch.setFormatter(formatter) + logger.addHandler(ch) + + +def neighbors(field, i, j, fsize): + nsum = 0 + for l in range(1, 10): + x = i - 1 + (l - 1) // 3 + y = j - 1 + (l + 2) % 3 + if -1 < x < fsize and -1 < y < fsize and field[x][y] == 1: + nsum += 1 + nsum -= field[i][j] + return nsum + + +def neighbors_cyclo(field, i, j, fsize): + nsum = 0 + for l in range(9): + x = (i - 1 + l // 3) % fsize + y = (j - 1 + l % 3) % fsize + nsum += field[x][y] + nsum -= field[i][j] + return nsum + + +def nextGen(field, fsize): + tmp_field = deepcopy(field) + for i in range(fsize): + for j in range(fsize): + neighb = neighbors(tmp_field, i, j, fsize) + if field[i][j] == 1 and not (2 <= neighb <= 3): + field[i][j] = 0 + elif field[i][j] == 0 and neighb == 3: + field[i][j] = 1 + + +def uniqueRows(data): + uniq = np.unique(data.view(data.dtype.descr * data.shape[1])) + return uniq.view(data.dtype).reshape(-1, data.shape[1]) + + +def generateData(board_size, count=10**5): + assert(2**(board_size**2) >= count) + X = np.random.randint(2, size=(int(count*1.2),board_size*board_size)) + X = uniqueRows(X)[:count] + Y = [] + for row in X: + tmp_list = row.reshape((board_size,board_size)).tolist() + nextGen(tmp_list, board_size) + Y.append(tmp_list) + return (X, np.asarray(Y).reshape(X.shape)) + + +def loadKeras(path): + model = keras.models.model_from_json(open(path + '.json').read()) + model.load_weights(path + '.h5') + model.compile(loss='MSE', optimizer='nadam', metrics=[]) + + logging.debug("Keras model loaded from {}".format(path)) + return model + + +def saveKeras(model, path): + json_architecture = model.to_json() + json_path = path + '.json' + with open(json_path, 'w') as f: + f.write(json_architecture) + weights_path = path + '.h5' + model.save_weights(weights_path, overwrite=True) + + +def getModel(n): + nn = Sequential() + nn.add(Dense(5*n**2, input_dim=n**2, init="normal", activation="sigmoid")) + #nn.add(Dropout(0.2)) # model without dropout because need simple + nn.add(Dense(4*n**2,init="normal", activation="sigmoid")) + #nn.add(Dropout(0.15)) + nn.add(Dense(n**2,init="normal", activation="sigmoid")) + nn.compile(loss="MSE", optimizer="nadam", metrics=[]) + return nn + + +def getAccuracies(model,x_test,y_test): + preds = model.predict(x_test) + preds = np.rint(preds).astype("int") + acc_square = 1.0 * (preds == y_test).sum() / y_test.size + acc_boards = 0 + for pred, real in zip(preds, y_test): + if (pred != real).sum() == 0: + acc_boards += 1 + acc_boards = 1.0 * acc_boards / y_test.shape[0] + return (acc_square, acc_boards) + + + +META_PARAMETERS = { + 5:[1600*4**i for i in range(6)], + 6:[1600*4**i for i in range(6)], + 8:[1600*4**i for i in range(6)], + 9:[1600*4**i for i in range(6)], + 10:[1600*4**i for i in range(6)], +} + + +if __name__ == "__main__": + initLogging() + + plt.title("Neural Life") + + plt.xscale("log") + + plt.xlabel("Train size") + plt.ylabel("Cell accuracy") + + plt_patches = [] + for meta_ind,N in enumerate(sorted(META_PARAMETERS.keys())): + points_x = [] + points_y = [] + for data_size in META_PARAMETERS[N]: + cur_time = datetime.now() + + X_train, X_test, Y_train, Y_test = train_test_split( + *generateData(N, data_size), # X and Y + test_size=0.6, + random_state=23 + ) + + train_size = X_train.shape[0] + + nn = getModel(N) + + nn.fit(X_train, Y_train, nb_epoch=40, shuffle=False, verbose=0) + + cellAcc, boardAcc = getAccuracies(nn, X_test, Y_test) + + points_x.append(train_size) + points_y.append(cellAcc) + + logging.info(("for board {}x{} with train size={} cell accuracy is {:.5f}%, " + + "board accuracy is {:.5f}% and delta with theoretical board accuracy " + + "is {:.8f}% it takes {}").format( + N, + N, + train_size, + 100 * cellAcc, + 100 * boardAcc, + 100 * abs(boardAcc - cellAcc**(N**2)), + datetime.now() - cur_time + )) + saveKeras(nn, "models/model_{}_{}".format(N,train_size)) + plt.plot(points_x, points_y, "o", linestyle="-", color=cm.ocean(meta_ind/len(META_PARAMETERS))) + plt_patches.append(mpatches.Patch(color=cm.ocean(meta_ind/len(META_PARAMETERS)), label="N={}".format(N))) + + plt.legend(handles=plt_patches) + plt.savefig("graphics.svg") diff --git a/plotboardacc.py b/plotboardacc.py new file mode 100644 index 0000000..caacee8 --- /dev/null +++ b/plotboardacc.py @@ -0,0 +1,46 @@ +#!/usr/bin/python +# -*- coding: utf-8 -*- + +__author__ = "Aleksey Lobanov" +__copyright__ = "Copyright 2016, Aleksey Lobanov" +__credits__ = ["Aleksey Lobanov"] +__license__ = "MIT" +__maintainer__ = "Aleksey Lobanov" +__email__ = "i@likemath.ru" + +import matplotlib.pyplot as plt +import matplotlib.cm as cm +import matplotlib.patches as mpatches + +from neurallife import loadKeras, generateData, getAccuracies, META_PARAMETERS + + +if __name__ == "__main__": + plt.title("Neural Life") + + plt.xscale("log") + plt.yscale("log") + + plt.xlabel("Train size") + plt.ylabel("Board accuracy") + + plt_patches = [] + for meta_ind,N in enumerate(sorted(META_PARAMETERS.keys())): + points_x = [] + points_y = [] + + X_test, Y_test = generateData(N, 100000) + + for data_size in META_PARAMETERS[N]: + nn = loadKeras("models/model_{}_{}".format(N, int(data_size * 0.5))) + + cellAcc, boardAcc = getAccuracies(nn, X_test, Y_test) + + points_x.append(data_size * 0.5) + points_y.append(boardAcc) + + plt.plot(points_x, points_y, "o", linestyle="-", color=cm.ocean(meta_ind/len(META_PARAMETERS))) + plt_patches.append(mpatches.Patch(color=cm.ocean(meta_ind/len(META_PARAMETERS)), label="N={}".format(N))) + + plt.legend(handles=plt_patches, loc=2) + plt.savefig("graphics-board.svg")