Произвольные комбинации параметров

Несколько читателей, включая Д. Эммануэла из Оук-Брука, шт. Иллинойс, Р. Файзела из Форт-Вашингтона, шт. Мэриленд, и Дж. Лью из Исследовательского центра Т. Уотсона фирмы IBM в Йорктаун- Хайтсе, шт. Нью-Йорк, описали в своих письмах современные теории, помогающие анализировать экологию планеты Аква-Тор. Пока у меня еще нет окончательного вывода по вопросу о том, помогут ли нам стохастические матрицы в выводе частных вероятностей выживания при произвольных комбинациях параметров. Однако интересно отметить, что дополнительно были исследованы уравнения Лотки-Вольтерра (сформулированные в 1931 г.), чтобы рассмотреть роль диффузии как фактора, влияющего как на хищника, так и на его жертву. Диффузия превращает гладко меняющиеся решения Лотки — Вольтерра в кривые более сложной формы. Исторические сведения, приведенные в письме Лью, свидетельствуют, что Альфред Дж. Лотка был американским математиком, который десятью годами раньше, чем Вольтерра, сформулировал эти уравнения.

Бойд воспользовался фазовой диаграммой, чтобы проанализировать динамику популяций акулы/рыбы. В каждый момент времени г откладываются текущие значения величин х — численности рыб и у — численности акул, как координаты точки на плоскости. По мере увеличения времени популяции описывают цикл, и точки на диаграмме рисуют замкнутую кривую причудливой формы вокруг фиксированного центра или фокуса. Бойл применил этот метод, чтобы изучить влияние размеров океана на выживаемость популяций. Он сообщает, что «в мирах более прямоугольной формы кривые на диаграмме утрачивают ярко выраженный фокус, траектории становятся более неровными и в конце концов приобретают совершенно случайный характер». Квадратная форма океана, очевидно, является предпочтительной.

Среди новшеств, введенных читателями, были такие, как жизнеспособность акул, мутации, двойные популяции рыб и планктон. В предыдущей статье, посвященной этой игре, я забыл упомянуть, что рыбы планеты Аква-Тор питаются вездесущим и изобилующим океаническим планктоном. Лемон ввел это свойство явным образом, поместив планктон в каждую точку океана, не занятую рыбой или акулой. Планктон размножается в свободных областях и играет ту же роль по отношению к рыбе, что рыба играет по отношению к акулам. Здесь также существуют вечные популяции.



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