Computer Recreations - Speaker Deck

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Computer Recreations OR, REDISCOVERING THE 1980S FOR PROGRAMMING FUN Andrew Kuchling amk @ amk.ca speakerdeck.com/akuchling/computer-recreations

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Photo by Colm Mulcahy

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#1: Cellular automata 4 5 4 1 0 4 3 5 1 (N = 6) If a cell is in state n, And has a neighbour in state n+1, Then the cell changes to state n+1

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#1: Cellular automata 4 5 4 1 0 4 3 5 1 5 0 5 1 1 4 4 0 1

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@classmethod def __init__(self, width=WIDTH, height=HEIGHT): self.board = {} self.width = width self.height = height for i in range(width): for j in range(height): board.board[(i,j)] = random.randrange( 0, NUM_STATES)

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def step(self): ”Do one iteration step of the cellular automaton" new = self.board.copy() for i in range(self.width): for j in range(self.height): new[(i,j)] = self.cell_rule(i, j) self.board.update(new)

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def cell_rule_4_cell_neighbourhood(self, x, y): "Evaluate the rule for a single cell…” value = self.board[x,y] successor = (value + 1) % NUM_STATES for (i, j) in [(-1, 0), (1, 0), (0, -1), (0, 1)]: neighb = self.board.get((x+i, y+j)) if neighb == successor: return successor else: return value

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01011001 11001011 #2: The evolution of flibs

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01011001 11001011 Result: 5 matches of 8 = 62%

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1B1C0C0B1A0A

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1 B 1 C 0 C 0 B 1 A 0 A 1 B 0 A 1 A 1 C 0 B 0 C

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1 B 1 C 0 C 0 B 1 A 0 A 1 B 0 A 1 A 1 C 0 B 0 C

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1 B 1 C 0 C 0 B 1 A 0 A 1 B 0 A 1 A 1 C 0 B 0 C 1 B 1 A 1 A 1 C 0 A 0 A

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Generation 0 Best score in pool: 75% Environment = 00100110100010011010 Prediction = 01000100100110010010 Worst score in pool: 20% Environment = 00100110100010011010 Prediction = 11101101011101110101

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Generation 100 Best score in pool: 90% Environment = 00100110100010011010 Prediction = 00100100100010010010 Worst score in pool: 45% Environment = 00100110100010011010 Prediction = 10001100011110110110

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Generation 1500 Best score in pool: 95% Environment = 00100110100010011010 Prediction = 00100110100110011010 Worst score in pool: 50% Environment = 00100110100010011010 Prediction = 00001000110000100011

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Perfect score found! In 5248 generations Environment = 00100110100010011010 Prediction = 00100110100010011010 0 1 A D,0 B,0 B A,0 C,0 C A,1 A,1 D E,1 B,1 E F,0 E,0 F D,1 B,1

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" = −1 or " = −1 (+) (+) = (+) (+) (－) = (－) (+) = (－) (－) (－) = (－) #3: Iterated functions

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>>> c = 0.5 + 2j ; c (0.5+2j) >>> c2 = complex(1,3) ; c2 (1+3j) >>> c2.real, c2.imag (1.0, 3.0) >>> abs(c2) 3.1622776601683795

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, = ,-. " + Now, repeat: 0 = 0 Pick a complex number

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, = ,-. " + 0 = 0 = 0.1 n Zn 1 0.1 2 0.11 3 0.1121 4 0.11256641 5 0.112671196660288 6 0.112694798556861 7 0.112700117621771 55

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, = ,-. " + 0 = 0 = -1.5 + 0.5j n Zn 1 -1.5 + 0.5j 2 0.5 - 1j 3 -2.25 - 0.5j 4 3.3125 + 2.75j 5 1.9101+ 18.71875j 6 -348.24 + 72.01j 7 116085 -50154j

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, = ,-. " + 0 = 0 = 0.1 + 0.4j n Zn 1 0.1 + 0.4j 2 -0.05 + 0.48j 3 0.1279 + 0.352j 4 0.00754559 + 0.3099584j 5 0.0039827261978 + 0.3953223619930j 6 0.0562639077838 + 0.4031489214554j 7 -0.059363425551 + 0.3546345325201j

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def iterate(c, max_iterations=100): "Iterates z**2 + c, for up to max_iterations” z = 0j for i in range(max_iterations): z = z**2 + c if abs(z) > 2.0: return (i+1) else: return 0

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def compute_grid(self, im_width, im_height): cx, cy = self.get_center() x_inc, y_inc = (self.width / (im_width / 2), …) grid = np.zeros((im_width, im_height)) for i in range(im_width): for j in range(im_height): coord = complex((cx - self.width) + i * x_inc, (cy - self.height) + j * y_inc) count = iterate(coord) grid[i,j] = count return grid

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# Vectorized code from Jean-Francois Puget def compute_grid_vectorized(self,im_width,im_height,maxiter=100): # … set up np.linspace() for x and y … c = np.array([complex(x,y) for x in rx for y in ry]) c = c.reshape((im_width,im_height)) grid = np.zeros(c.shape) z = np.zeros(c.shape, np.complex64) for it in range(maxiter): notdone = np.less(z.real*z.real + z.imag*z.imag, 4.0) grid[notdone] = it z[notdone] = z[notdone]**2 + c[notdone] return grid