{"slug":"chaos-maps","title":{"ja":"カオス写像","en":"Chaos maps"},"summary":{"ja":"単純な式をくり返すと秩序から混沌へ移る様子を、分岐図やクモの巣図の線で描く。","en":"How repeating a simple formula moves from order to chaos, drawn as bifurcation and cobweb diagrams."},"categories":["art","design","motion"],"subAspects":["generative.technique"],"aspects":["generative"],"tags":["chaos","logistic-map","bifurcation","cobweb"],"palette":[{"name":"Black","hex":"#05060A","ratio":0.82},{"name":"Cyan","hex":"#3FD9EC","ratio":0.09},{"name":"Green","hex":"#5BE38A","ratio":0.06},{"name":"Crimson","hex":"#E0405A","ratio":0.03}],"keywords":["bifurcation diagram","logistic map","cobweb plot","period doubling","chaos theory"],"traits":{"en":["A cloud of fine points traces how the long-run value of a formula splits as a parameter grows: one branch, then two, four, and a dense band","Inside the chaotic band, thin empty windows appear where order briefly returns","A zigzag cobweb line bounces between a curve and a diagonal line beside it","Fine glowing points and lines on black, without axes or labels","In motion, the parameter sweeps and the cobweb settles or wanders"],"ja":["細かな点の雲が、パラメータが増えるにつれて式の行き着く値が分かれていく様子をなぞる：1本、2本、4本、そして密な帯","混沌の帯の中に、秩序が一時的に戻る細い空白の窓がある","クモの巣状のジグザグの線が、曲線と対角線の間を行き来する","黒の地に細かく光る点と線で、軸やラベルはない","動きでは、パラメータが動き、クモの巣が落ち着いたりさまよったりする"]},"prompt":"Chaos map: a bifurcation diagram of fine glowing points splitting from one branch into two, four and a dense chaotic band with thin empty windows, beside a zigzag cobweb line bouncing between a curve and a diagonal, cyan and green on black, without axes or labels. As video, the parameter sweeps.","negativePrompt":"graph paper, axes and numbers, textbook figure, thick lines, white background","contrasts":[{"slug":"strange-attractor","title":{"ja":"ストレンジアトラクター","en":"Strange attractor"},"difference":{"en":"A strange attractor shows one chaotic trajectory as a dense, continuous winged form built from thousands of thin passes. Chaos maps are diagrams of an iterated formula: bifurcation trees and cobweb plots on axes, read as charts rather than as a single sculptural shape.","ja":"ストレンジアトラクタは、1本のカオス的な軌道を細い線で何千回も重ね、翼のような連続した形として見せる。カオス写像は反復する式の図で、分岐図やクモの巣図を座標軸の上に描く。1つの立体的な形ではなく、図表として読むもの。"}}],"images":[],"references":[{"label":"py5-media-art — kinetic_logistic_cobweb_chaos_3d","url":"https://github.com/asamiile/py5-media-art/tree/main/sketch/kinetic_logistic_cobweb_chaos_3d"},{"label":"py5-media-art — kinetic_kuramoto_chimera_states_2d","url":"https://github.com/asamiile/py5-media-art/tree/main/sketch/kinetic_kuramoto_chimera_states_2d"}],"links":{"page":{"ja":"https://visual-gallery.asami.tokyo/ja/styles/chaos-maps","en":"https://visual-gallery.asami.tokyo/en/styles/chaos-maps"},"json":"https://visual-gallery.asami.tokyo/api/v1/styles/chaos-maps","markdown":"https://visual-gallery.asami.tokyo/api/v1/styles/chaos-maps/md"}}