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February 21, 2021 01:41
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# The Fibonacci Network: Jupyter Notebook Companion\n", | |
"\n", | |
"This notebook is a supplemental to the Fibonacci Network blog post [here](https://blog.jordan.matelsky.com/fib-graph/)." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"from collections import Counter\n", | |
"import numpy as np\n", | |
"import networkx as nx" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Here, we generate the Fibonacci matrix derived from the Cassini/Catalan identity, as well as three other higher-order Fibonacci-like adjacency matrices." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"fib_graph = np.array([\n", | |
" [1, 1],\n", | |
" [1, 0],\n", | |
"])\n", | |
"\n", | |
"trib_graph = np.array([\n", | |
" [1, 1, 1],\n", | |
" [0, 0, 1],\n", | |
" [1, 0, 0]\n", | |
"])\n", | |
"\n", | |
"tetra_graph = np.array([\n", | |
" [1, 1, 1, 1],\n", | |
" [0, 0, 1, 0],\n", | |
" [0, 0, 0, 1],\n", | |
" [1, 0, 0, 0]\n", | |
"])\n", | |
"\n", | |
"tenba_graph = np.array([\n", | |
" [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n", | |
" [0, 0, 1, 0, 0, 0, 0, 0, 0, 0],\n", | |
" [0, 0, 0, 1, 0, 0, 0, 0, 0, 0],\n", | |
" [0, 0, 0, 0, 1, 0, 0, 0, 0, 0],\n", | |
" [0, 0, 0, 0, 0, 1, 0, 0, 0, 0],\n", | |
" [0, 0, 0, 0, 0, 0, 1, 0, 0, 0],\n", | |
" [0, 0, 0, 0, 0, 0, 0, 1, 0, 0],\n", | |
" [0, 0, 0, 0, 0, 0, 0, 0, 1, 0],\n", | |
" [0, 0, 0, 0, 0, 0, 0, 0, 0, 1],\n", | |
" [1, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n", | |
"])" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"You _could_ derive the sequences below by taking powers of the matrices (in `numpy` syntax, the `@` operator)." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"array([[2, 1],\n", | |
" [1, 1]])" | |
] | |
}, | |
"execution_count": 3, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"fib_graph@fib_graph" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Here, I use the `networkx` library to simulate a walk of length `n` using the weights above as the transition matrix. Note that this is a way slower way of deriving the same numbers, but kinda a cute illustration of what's going on." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"class Walker:\n", | |
" \n", | |
" def __init__(self, g: nx.Graph, start_node: int = 0):\n", | |
" self._g = g\n", | |
" self._start_node = start_node\n", | |
" self._marching_front = start_node if isinstance(start_node, list) else [start_node] \n", | |
" self._steps = 0\n", | |
" \n", | |
" def _step(self):\n", | |
" marching_front = []\n", | |
" for node in self._marching_front:\n", | |
" marching_front.extend(self._g.neighbors(node))\n", | |
" self._marching_front = marching_front\n", | |
" self._steps += 1\n", | |
" \n", | |
" def reset(self):\n", | |
" self._marching_front = self._start_node if isinstance(self._start_node, list) else [self._start_node] \n", | |
" self._steps = 0\n", | |
" \n", | |
" def get_landing_nodes(self, walk_length: int):\n", | |
" while self._steps < walk_length:\n", | |
" self._step()\n", | |
" return self._marching_front\n", | |
" \n", | |
" \n", | |
"def get_walker_sequence(matrix: np.array, n: int = 20):\n", | |
" \"\"\"\n", | |
" Get the integer sequence for all 0..n steps on the graph\n", | |
" (in other words, up to the nth Fibonacci number).\n", | |
" \"\"\"\n", | |
" s = []\n", | |
" G = nx.from_numpy_array(matrix, create_using=nx.DiGraph)\n", | |
" w = Walker(G, [0])\n", | |
" for i in range(n):\n", | |
" s.append(Counter(w.get_landing_nodes(i))[1])\n", | |
" w.reset()\n", | |
" return s\n", | |
" " | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Finally, generate the sequences. By default, these generate the first 20 integers." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"fib_numbers = get_walker_sequence(fib_graph)\n", | |
"trib_numbers = get_walker_sequence(trib_graph)\n", | |
"tetra_numbers = get_walker_sequence(tetra_graph)\n", | |
"tenba_numbers = get_walker_sequence(tenba_graph)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Plot the sequences, along powers of two, for illustration." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import matplotlib.pyplot as plt" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"<matplotlib.legend.Legend at 0x13be6d310>" | |
] | |
}, | |
"execution_count": 8, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<Figure size 900x600 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.figure(figsize=(6, 4), dpi=150)\n", | |
"plt.plot(fib_numbers, marker='.', linewidth=0.5, label=\"Fibonacci\")\n", | |
"plt.plot(trib_numbers, marker='.', linewidth=0.5, label=\"Tribonacci\")\n", | |
"plt.plot(tetra_numbers, marker='.', linewidth=0.5, label=\"Tetranacci\")\n", | |
"plt.plot(tenba_numbers, marker='.', linewidth=0.5, label=\"Ten-banacci\")\n", | |
"plt.plot([2**n for n in range(18)], marker='.', linewidth=0.5, label=\"Powers of Two\")\n", | |
"# plt.yscale(\"log\")\n", | |
"plt.xticks(range(20))\n", | |
"plt.legend()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.7.7" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 4 | |
} |
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