Mechanical harmonic chaos game

Abstract

We consider an analogue in classical mechanics to Barnsley’s chaos game in which a particle acts as a (possibly damped) harmonic oscillator whose centre of attraction randomly changes at fixed time intervals. This system exhibits a rich behaviour depending on the relationship between the strength of the attractive force and the drag force. We show how this mechanical system includes Barnsley’s (discrete) chaos game, producing for example the Sierpinski gasket, and in addition we observe evolutions which have interesting symmetries not exhibited by the Barnsley game. The system also provides a classical analogue of the quantum chaos game previously investigated by the current authors.

Subtle dynamics of the chaotic torsion pendulum: a detailed comparison between experiments and numerical simulations

“…The seeming contradiction between the deterministic process and the unpredictable behavior of chaos offers an interesting and valuable general insight into the nonlinear nature of the world. Research on the topic of chaos is flourishing since its discovery, not only from the perspective of advanced science [2][3][4][5][6][7], but also from an educational point of view [8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Many excellent introductory monographs that explain basic concepts of chaos exist [8][9][10][11][12][13][14][15], as well as various elaborate devices [16][17][18][19][20][21] that vividly depict the dynamical feature of a chaotic system.…”

“…Research on the topic of chaos is flourishing since its discovery, not only from the perspective of advanced science [2][3][4][5][6][7], but also from an educational point of view [8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Many excellent introductory monographs that explain basic concepts of chaos exist [8][9][10][11][12][13][14][15], as well as various elaborate devices [16][17][18][19][20][21] that vividly depict the dynamical feature of a chaotic system. In college-level physics courses, one of the standard devices for exhibiting chaotic behavior is the chaotic torsion pendulum (CTP) [22][23][24][25].…”

Randomly evolving Platonic Solids: a zero-player game

“…In particular we have found inspiration in incorporating various physical ideas within puzzles and games. Our work has lead us to relatively simple problems [6,7] and more advanced papers [8][9][10].…”