Предисловие ....................................................................................................................................................................................................8
Для кого эта книга? ............................................................................................................................................................................... 9
Изменения после выхода первого издания................................................................................................................................ 9
Использование кода ...........................................................................................................................................................................10
Обозначения, используемые в этой книге.................................................................................................................................11
O'Reilly Safari..........................................................................................................................................................................................11
Как с нами связаться ..........................................................................................................................................................................12
Список лиц, принимавших участие в работе над книгой....................................................................................................12
Об авторе.................................................................................................................................................................................................13
Колофон ...................................................................................................................................................................................................13
Глава 1. Наука о сложных системах .....................................................................................................................................................14
Меняющиеся критерии науки.........................................................................................................................................................15
Оси научных моделей ........................................................................................................................................................................16
Разные модели для разных целей ................................................................................................................................................17
Инженерия сложных систем............................................................................................................................................................18
Доктрина сложных систем................................................................................................................................................................19
Глава 2. Графы................................................................................................................................................................................................21
Что такое графы?..................................................................................................................................................................................21
NetworkX..................................................................................................................................................................................................23
Случайные графы.................................................................................................................................................................................24
Генерация графов.................................................................................................................................................................................25
Связные графы......................................................................................................................................................................................26
Генерация графов Эрдёша–Реньи ................................................................................................................................................27
Вероятность связности.......................................................................................................................................................................29
Анализ алгоритмов графов ..............................................................................................................................................................30
Упражнения ............................................................................................................................................................................................31
Глава 3. Графы «Мир тесен».....................................................................................................................................................................33
Стэнли Милгрэм....................................................................................................................................................................................33
Ваттс и Строгац .....................................................................................................................................................................................34
Кольцевая решетка..............................................................................................................................................................................34
Графы Ваттса–Строгаца.....................................................................................................................................................................36
Кластеризация.......................................................................................................................................................................................37
Длина кратчайшего пути...................................................................................................................................................................38
Эксперимент Ваттса–Строгаца.......................................................................................................................................................39
Что это за объяснение?......................................................................................................................................................................40
Поиск в ширину ....................................................................................................................................................................................41
Алгоритм Дейкстры .............................................................................................................................................................................43
Упражнения ............................................................................................................................................................................................44
Глава 4. Безмасштабные сети..................................................................................................................................................................46
Данные социальных сетей................................................................................................................................................................46
Модель Ваттса–Строгаца ..................................................................................................................................................................48
6 Изучение сложных систем с помощью Python
Степень .....................................................................................................................................................................................................48
Распределения с тяжелыми хвостами .........................................................................................................................................50
Модель Барабаши–Альберта...........................................................................................................................................................51
Генерация графов Барабаши–Альберта.....................................................................................................................................53
Интегральные распределения ........................................................................................................................................................54
Объяснительные модели...................................................................................................................................................................56
Упражнения ............................................................................................................................................................................................57
Глава 5. Клеточные автоматы .................................................................................................................................................................59
Простой клеточный автомат............................................................................................................................................................59
Эксперимент Вольфрама...................................................................................................................................................................59
Классификация клеточных автоматов.........................................................................................................................................60
Хаотичность............................................................................................................................................................................................61
Детерминизм..........................................................................................................................................................................................62
Космические корабли.........................................................................................................................................................................64
Универсальность...................................................................................................................................................................................65
Фальсифицируемость.........................................................................................................................................................................66
Что это за модель?...............................................................................................................................................................................67
Реализация клеточных автоматов.................................................................................................................................................68
Взаимная корреляция ........................................................................................................................................................................69
Таблицы клеточных автоматов.......................................................................................................................................................71
Упражнения ............................................................................................................................................................................................71
Глава 6. Игра «Жизнь»................................................................................................................................................................................73
Игра «Жизнь» Конвея.........................................................................................................................................................................73
Конструкции игры «Жизнь» .............................................................................................................................................................74
Гипотеза Конвея....................................................................................................................................................................................75
Реализм....................................................................................................................................................................................................76
Инструментализм.................................................................................................................................................................................77
Реализация игры «Жизнь»................................................................................................................................................................78
Упражнения ............................................................................................................................................................................................80
Глава 7. Физическое моделирование...................................................................................................................................................82
Диффузия ................................................................................................................................................................................................82
Реакция диффузии...............................................................................................................................................................................83
Перколяция.............................................................................................................................................................................................86
Фазовый переход.................................................................................................................................................................................88
Фракталы.................................................................................................................................................................................................89
Фракталы и перколяционные модели.........................................................................................................................................91
Упражнения ............................................................................................................................................................................................92
Глава 8. Самоорганизованная критичность.......................................................................................................................................94
Критические системы.........................................................................................................................................................................94
Песчаные кучи.......................................................................................................................................................................................95
Реализация песчаной кучи...............................................................................................................................................................95
Распределения с тяжелыми хвостами .........................................................................................................................................98
Фракталы.............................................................................................................................................................................................. 100
Розовый шум....................................................................................................................................................................................... 103
Звук песка ............................................................................................................................................................................................ 104
Редукционизм и холизм................................................................................................................................................................. 105
Содержание 7
Самоорганизованная критичность, причинность и прогнозирование........................................................................ 107
Упражнения ......................................................................................................................................................................................... 108
Глава 9. Агент-ориентированные модели.......................................................................................................................................110
Модель Шеллинга.............................................................................................................................................................................. 110
Реализация модели Шеллинга..................................................................................................................................................... 111
Сегрегация............................................................................................................................................................................................ 113
Sugarscape............................................................................................................................................................................................ 114
Имущественное неравенство....................................................................................................................................................... 116
Реализация Sugarscape................................................................................................................................................................... 117
Миграция и волновое поведение............................................................................................................................................... 119
Эмерджентность................................................................................................................................................................................. 119
Упражнения ......................................................................................................................................................................................... 121
Глава 10. Стаи, стада и пробки.............................................................................................................................................................122
Пробки................................................................................................................................................................................................... 122
Случайное возмущение.................................................................................................................................................................. 124
Boid ......................................................................................................................................................................................................... 125
Алгоритм Boids................................................................................................................................................................................... 126
Разрешение конфликтов................................................................................................................................................................ 128
Эмерджентность и свобода воли................................................................................................................................................ 129
Упражнения ......................................................................................................................................................................................... 130
Глава 11. Эволюция ..................................................................................................................................................................................131
Моделирование эволюции............................................................................................................................................................ 131
Адаптивный ландшафт.................................................................................................................................................................... 132
Агенты.................................................................................................................................................................................................... 133
Моделирование ................................................................................................................................................................................. 133
Нет дифференциации...................................................................................................................................................................... 134
Свидетельство эволюции............................................................................................................................................................... 135
Дифференциальное выживание................................................................................................................................................. 137
Мутация................................................................................................................................................................................................. 138
Видообразование.............................................................................................................................................................................. 140
Резюме................................................................................................................................................................................................... 142
Упражнения ......................................................................................................................................................................................... 143
Глава 12. Эволюция кооперации ........................................................................................................................................................144
Дилемма заключенного.................................................................................................................................................................. 144
Проблема альтруизма ..................................................................................................................................................................... 145
Чемпионаты по дилемме заключенного................................................................................................................................. 146
Моделирование эволюции кооперации.................................................................................................................................. 147
Класс Tournament.............................................................................................................................................................................. 148
Класс Simulation................................................................................................................................................................................ 150
Результаты............................................................................................................................................................................................ 150
Выводы.................................................................................................................................................................................................. 153
Упражнения ......................................................................................................................................................................................... 154
Приложение A. Список литературы ...................................................................................................................................................156
Указатель ......................................................................................................................................................................................................157