{"product_id":"chuanna-chuas-double-scroll-physics-t-shirt","title":"Chuanna – Chua's Double Scroll Physics T-Shirt","description":"\u003cp\u003eChuanna wires up five parts on her breadboard, and out spills a ribbon that loops around two points and never repeats.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eLeon Chua designed a simple autonomous electronic circuit in 1983: two capacitors, an inductor, a resistor and one piecewise-linear nonlinear resistor, the Chua diode. It oscillates chaotically. The orbit loops around two unstable equilibria and jumps irregularly between them, tracing the “double scroll”.\u003c\/p\u003e\u003cp\u003eWith the classic parameters a = 15.6, b = 28, m0 = −8\/7 and m1 = −5\/7, the dimensionless equations below give the double-scroll attractor.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003edx\/dt = α(y − x − f(x)),   dy\/dt = x − y + z,   dz\/dt = −βy\u003cbr\u003ef(x) = m₁x + ½(m₀ − m₁)(|x + 1| − |x − 1|)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ex, y, z: dimensionless capacitor voltages and inductor current\u003c\/li\u003e\n\u003cli\u003eα, β: dimensionless circuit parameters (a, b on the shirt)\u003c\/li\u003e\n\u003cli\u003em₀, m₁: inner and outer slopes of the Chua diode\u003c\/li\u003e\n\u003cli\u003et: dimensionless time\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eChua 1983; Matsumoto, IEEE TCAS 31, 1055 (1984) found the attractor in simulation; Chua, Komuro \u0026amp; Matsumoto, IEEE TCAS 33, 1072 (1986) proved chaos in the double scroll family.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The Chua diode is itself built from op-amps or diodes in practice, so “five parts” counts it as one. Chaos was proved in 1986, not 1983.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Chuanna, the pixel-art character, with “THE DOUBLE SCROLL”. Back: the three equations, the diode function, the classic parameters and the 1983, 1984 and 1986 sources. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50960509730919,"sku":"49173323190424447191","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50960509763687,"sku":"17378792486722328528","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50960509796455,"sku":"26558000878347010450","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50960509829223,"sku":"11417012767802885175","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50960509861991,"sku":"80825424804195731228","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50960509894759,"sku":"27005368485960366134","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50960509927527,"sku":"11425816552952445882","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50960509960295,"sku":"29666260600896489173","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50960509993063,"sku":"20895465322821005717","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50960510025831,"sku":"30282325217091118788","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50960510058599,"sku":"25318063985609034867","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50960510091367,"sku":"12106716874077651356","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50960510124135,"sku":"22312827667084897877","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50960510156903,"sku":"28632498929678447303","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50960510189671,"sku":"13679958554243211285","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50960510222439,"sku":"89442469505335921261","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/chua-circuit_front_01_white.png?v=1793625600","url":"https:\/\/pixelatedphysics.com\/pl\/products\/chuanna-chuas-double-scroll-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}