| When shown a flash of light, the neurons in a retina (of tiger salamander larvae or humans) exhibit a particular firing pattern, which stops shortly after the flash.((Crevier & Meister. //Synchronous Period-Doubling in Flicker of Salamander and Man.// Journal of Neurophysiology **79**. (1998) p. 1869-1878. [[https://journals.physiology.org/doi/pdf/10.1152/jn.1998.79.4.1869]].)) If the flash is shown periodically, with a frequency of less than 9 Hz, the retina’s response is periodic: each flash is followed by this particular firing pattern. When the frequency exceeds 9 Hz, there is not enough time for this pattern to complete, so every other response is different. The retina responds periodically, with a period double the period of the flashing light. When the frequency exceeds 12 Hz, the period doubles again and the retina’s response is the same only after every four flashes. When the frequency exceeds 15 Hz, the retina’s response is chaotic. The subjects say that the light appears “flickering.” This is a period doubling cascade, Feigenbaum’s classic route to chaos.((This is described in Section 9 of the accompanying report. \\ Heninger & Johnson. //Chaos and Intrinsic Unpredictability.// AI Impacts. [[http://aiimpacts.org/wp-content/uploads/2023/03/Chaos-and-Intrinsic-Unpredictability.pdf]]. \\ See also Wikipedia: [[https://en.wikipedia.org/wiki/Period-doubling_bifurcation|Period-doubling bifurcation]] or Scholarpedia: [[http://www.scholarpedia.org/article/Period_doubling|Period doubling]].)) Feigenbaum’s theory predicts that, with more precise control over the frequency of the flashing light, you could see the retina respond at 8 or 16 times the period of the flashing light, and that the period doubling bifurcations get closer together in a way characterized by Feigenbaum’s constants, before transitioning to chaos. | When shown a flash of light, the neurons in a retina (of tiger salamander larvae or humans) exhibit a particular firing pattern, which stops shortly after the flash.((Crevier & Meister. //Synchronous Period-Doubling in Flicker of Salamander and Man.// Journal of Neurophysiology **79**. (1998) p. 1869-1878. [[https://journals.physiology.org/doi/pdf/10.1152/jn.1998.79.4.1869]].)) If the flash is shown periodically, with a frequency of less than 9 Hz, the retina’s response is periodic: each flash is followed by this particular firing pattern. When the frequency exceeds 9 Hz, there is not enough time for this pattern to complete, so every other response is different. The retina responds periodically, with a period double the period of the flashing light. When the frequency exceeds 12 Hz, the period doubles again and the retina’s response is the same only after every four flashes. When the frequency exceeds 15 Hz, the retina’s response is chaotic. The subjects say that the light appears “flickering.” This is a period doubling cascade, Feigenbaum’s classic route to chaos.((This is described in Section 9 of the accompanying report. \\ Heninger & Johnson. //Chaos and Intrinsic Unpredictability.// AI Impacts. [[http://aiimpacts.org/wp-content/uploads/2023/04/Chaos-and-Intrinsic-Unpredictability.pdf]]. \\ See also Wikipedia: [[https://en.wikipedia.org/wiki/Period-doubling_bifurcation|Period-doubling bifurcation]] or Scholarpedia: [[http://www.scholarpedia.org/article/Period_doubling|Period doubling]].)) Feigenbaum’s theory predicts that, with more precise control over the frequency of the flashing light, you could see the retina respond at 8 or 16 times the period of the flashing light, and that the period doubling bifurcations get closer together in a way characterized by Feigenbaum’s constants, before transitioning to chaos. |
| The normal firing pattern of neurons in the olfactory bulb of rabbits is chaotic.((Di Prisco & Freeman. //Odor-related bulbar EEG spatial pattern analysis during appetitive conditioning in rabbits.// Behavioral Neuroscience **99.5**. (1985) [[https://escholarship.org/content/qt7s63p7sx/qt7s63p7sx.pdf]]. \\ Freeman & Di Prisco. //Spatial patterns differences with discriminated odors manifest chaotic and limit cycles attractors in olfactory bulb of rabbits.// Brain Theory. (1986) p. 97-119.)) When exposed to a smell the rabbit has previously learned, the firing patterns cease to be chaotic and instead become periodic. The periodic motion seems to follow one of the unstable periodic orbits embedded in the original strange attractor. Each smell the rabbit has previously learned corresponds to a different periodic orbit. It seems as though the olfactory bulb is using a kind of dynamical memory storage, which allows rapid responses to learned stimuli. The smells are remembered as unstable periodic orbits within the strange attractor. | The normal firing pattern of neurons in the olfactory bulb of rabbits is chaotic.((Di Prisco & Freeman. //Odor-related bulbar EEG spatial pattern analysis during appetitive conditioning in rabbits.// Behavioral Neuroscience **99.5**. (1985) [[https://escholarship.org/content/qt7s63p7sx/qt7s63p7sx.pdf]]. \\ Freeman & Di Prisco. //Spatial patterns differences with discriminated odors manifest chaotic and limit cycles attractors in olfactory bulb of rabbits.// Brain Theory. (1986) p. 97-119.)) When exposed to a smell the rabbit has previously learned, the firing patterns cease to be chaotic and instead become periodic. The periodic motion seems to follow one of the unstable periodic orbits embedded in the original strange attractor. Each smell the rabbit has previously learned corresponds to a different periodic orbit. It seems as though the olfactory bulb is using a kind of dynamical memory storage, which allows rapid responses to learned stimuli. The smells are remembered as unstable periodic orbits within the strange attractor. |
