{"product_id":"kit-4d-phase-space-trajectory","title":"4D Phase Space Trajectory Kit with ESP32","description":"\u003ch1\u003eESP32 4D Phase Space Trajectory Kit – Build an Animated Lorenz Attractor with Colour Time Axis\u003c\/h1\u003e\n\n\u003cp class=\"value-summary\"\u003eEvery part needed, pre-tested for compatibility, with an AI build companion trained on this exact project. Shipped from Bengaluru in 3-5 days.\u003c\/p\u003e\n\n\u003cdiv class=\"specs-strip\"\u003e\n  \u003cspan\u003e\u003cstrong\u003eDifficulty:\u003c\/strong\u003e Advanced\u003c\/span\u003e\n  \u003cspan\u003e\u003cstrong\u003eBuild Time:\u003c\/strong\u003e 6-8 hrs\u003c\/span\u003e\n  \u003cspan\u003e\u003cstrong\u003eAge:\u003c\/strong\u003e 21-24\u003c\/span\u003e\n  \u003cspan\u003e\u003cstrong\u003eSkill:\u003c\/strong\u003e Embedded systems \u0026amp; data visualization\u003c\/span\u003e\n\u003c\/div\u003e\n\n\u003cp\u003eTransform a set of differential equations into a living, breathing chaos machine. This kit places the Lorenz attractor—the most famous example of deterministic chaos—directly into your hands. The ESP32 crunches Runge-Kutta integration in real time, while the 2.4-inch TFT renders the evolving trajectory as a 3D projection. A fourth dimension, time, flows through the colour palette, creating a visualization you can tweak with potentiometers and enclose in a permanent, solder-built device.\u003c\/p\u003e\n\n\u003ch2\u003eWhat You'll Build\u003c\/h2\u003e\n\u003cp\u003eYou’ll assemble a standalone embedded system that computes the Lorenz system and displays its phase-space evolution. The device runs autonomously: turn it on, and the iconic butterfly wings appear instantly. Adjusting the two potentiometers changes the viewing angle and simulation speed, while the colour gradient from deep violet to bright yellow traces history, making the chaotic orbit legible as a 4D trajectory.\u003c\/p\u003e\n\n\u003ch2\u003eWhat You'll Learn\u003c\/h2\u003e\n\u003cul\u003e\n  \u003cli\u003eImplement numerical integration (fourth-order Runge-Kutta) on a constrained microcontroller\u003c\/li\u003e\n  \u003cli\u003eRender 3D point clouds on an SPI TFT using optimized projection math\u003c\/li\u003e\n  \u003cli\u003eMap time to a continuous colour axis for genuine 4‑D visualization\u003c\/li\u003e\n  \u003cli\u003eDesign and solder a permanent electronics enclosure from a prototyping board\u003c\/li\u003e\n\u003c\/ul\u003e\n\n\u003ch2\u003eKit Contents\u003c\/h2\u003e\n\u003ctable\u003e\n  \u003cthead\u003e\u003ctr\u003e\n\u003cth\u003eComponent\u003c\/th\u003e\n\u003cth\u003eQuantity\u003c\/th\u003e\n\u003c\/tr\u003e\u003c\/thead\u003e\n  \u003ctbody\u003e\n    \u003ctr\u003e\n\u003ctd\u003eESP32 Dev Board\u003c\/td\u003e\n\u003ctd\u003e1\u003c\/td\u003e\n\u003c\/tr\u003e\n    \u003ctr\u003e\n\u003ctd\u003e2.4in TFT ILI9341\u003c\/td\u003e\n\u003ctd\u003e1\u003c\/td\u003e\n\u003c\/tr\u003e\n    \u003ctr\u003e\n\u003ctd\u003eTactile Button\u003c\/td\u003e\n\u003ctd\u003e2\u003c\/td\u003e\n\u003c\/tr\u003e\n    \u003ctr\u003e\n\u003ctd\u003e10kΩ Potentiometer\u003c\/td\u003e\n\u003ctd\u003e2\u003c\/td\u003e\n\u003c\/tr\u003e\n    \u003ctr\u003e\n\u003ctd\u003e100nF Caps\u003c\/td\u003e\n\u003ctd\u003e5\u003c\/td\u003e\n\u003c\/tr\u003e\n    \u003ctr\u003e\n\u003ctd\u003ePCB Prototype Board\u003c\/td\u003e\n\u003ctd\u003e2\u003c\/td\u003e\n\u003c\/tr\u003e\n    \u003ctr\u003e\n\u003ctd\u003e5V 2A PSU\u003c\/td\u003e\n\u003ctd\u003e1\u003c\/td\u003e\n\u003c\/tr\u003e\n    \u003ctr\u003e\n\u003ctd\u003eEnclosure Box\u003c\/td\u003e\n\u003ctd\u003e1\u003c\/td\u003e\n\u003c\/tr\u003e\n    \u003ctr\u003e\n\u003ctd\u003eSoldering Iron\u003c\/td\u003e\n\u003ctd\u003e1\u003c\/td\u003e\n\u003c\/tr\u003e\n    \u003ctr\u003e\n\u003ctd\u003eSolder Wire\u003c\/td\u003e\n\u003ctd\u003e1\u003c\/td\u003e\n\u003c\/tr\u003e\n  \u003c\/tbody\u003e\n\u003c\/table\u003e\n\n\u003ch2\u003eWhy Buy This Kit Instead of Sourcing Parts Separately\u003c\/h2\u003e\n\u003ctable\u003e\n  \u003cthead\u003e\u003ctr\u003e\n\u003cth\u003eFactor\u003c\/th\u003e\n\u003cth\u003eSourcing Separately\u003c\/th\u003e\n\u003cth\u003eCompoden Kit\u003c\/th\u003e\n\u003c\/tr\u003e\u003c\/thead\u003e\n  \u003ctbody\u003e\n    \u003ctr\u003e\n\u003ctd\u003eCompatibility checks\u003c\/td\u003e\n\u003ctd\u003eYou verify every part\u003c\/td\u003e\n\u003ctd\u003ePre-tested as a system\u003c\/td\u003e\n\u003c\/tr\u003e\n    \u003ctr\u003e\n\u003ctd\u003eBuild support\u003c\/td\u003e\n\u003ctd\u003eForums and scattered tutorials\u003c\/td\u003e\n\u003ctd\u003eAI companion trained on this exact project\u003c\/td\u003e\n\u003c\/tr\u003e\n    \u003ctr\u003e\n\u003ctd\u003eTime to first working build\u003c\/td\u003e\n\u003ctd\u003eDays of debugging\u003c\/td\u003e\n\u003ctd\u003eHours, with step-by-step guidance\u003c\/td\u003e\n\u003c\/tr\u003e\n    \u003ctr\u003e\n\u003ctd\u003eShipping coordination\u003c\/td\u003e\n\u003ctd\u003eMultiple sellers, multiple delays\u003c\/td\u003e\n\u003ctd\u003eOne shipment from Bengaluru in 3-5 days\u003c\/td\u003e\n\u003c\/tr\u003e\n  \u003c\/tbody\u003e\n\u003c\/table\u003e\n\n\u003ch2\u003eWho This Kit Is For\u003c\/h2\u003e\n\u003cp\u003eFinal-year B.Tech students in ECE, EEE, or CS exploring nonlinear dynamics will find a ready-made capstone project. Smart India Hackathon hardware-track teams can fork it as a live demo of embedded computation. Physics enthusiasts and researchers who want a tangible, always-running visualization of the butterfly effect will appreciate the soldered, permanent enclosure. This kit also fits advanced ATL tinkering mentors and IIT\/NIT fest project displays.\u003c\/p\u003e\n\n\u003ch2\u003eBuilt and Backed by Compoden\u003c\/h2\u003e\n\u003cp\u003eEvery Compoden kit ships with an AI build companion trained on this exact project — accessible via a QR code on the box, with WhatsApp and email backup. We've spent 10 years building projects for makers, schools, and institutions across India. If a part fails because of a manufacturing defect, replace it free within 7 days.\u003c\/p\u003e\n\n\u003cdetails\u003e\u003csummary\u003eWhat if I get stuck during the build?\u003c\/summary\u003e\u003cp\u003eThe AI companion covers every solder joint and code upload. If you still need help, WhatsApp support from our Bengaluru team responds within hours.\u003c\/p\u003e\u003c\/details\u003e\n\u003cdetails\u003e\u003csummary\u003eWhat is the Lorenz attractor and why visualize it in 4D?\u003c\/summary\u003e\u003cp\u003eThe Lorenz system is a set of three differential equations that model atmospheric convection, famous for its chaotic, butterfly-shaped trajectory. Adding colour as a time axis reveals the order hidden in chaos—showing which regions the trajectory visits most and how it orbits unstable equilibrium points.\u003c\/p\u003e\u003c\/details\u003e\n\u003cdetails\u003e\u003csummary\u003eDoes this kit require prior soldering experience?\u003c\/summary\u003e\u003cp\u003eIt is designed for advanced builders; you will solder all components onto prototyping boards. Basic through-hole soldering skill is assumed. The AI companion includes close-up images of every joint to guide you.\u003c\/p\u003e\u003c\/details\u003e\n\u003cdetails\u003e\u003csummary\u003eCan I modify the simulation parameters?\u003c\/summary\u003e\u003cp\u003eAbsolutely. The source code (provided via the AI companion) lets you change the Prandtl, Rayleigh, and Beta constants. The two potentiometers are mapped to view angle and speed, and you can reassign them to any runtime variable.\u003c\/p\u003e\u003c\/details\u003e\n\n\u003cdiv class=\"kit-description\"\u003e\n  \u003cp\u003eLorenz attractor computed on ESP32 and rendered as animated 3D projection on TFT with colour time axis.\u003c\/p\u003e\n  \u003ch4\u003eWhat's in this kit\u003c\/h4\u003e\n  \u003cul\u003e\n    \u003cli\u003e\u003ca href=\"\/products\/esp32-30-pin-development-board-cp2102-wifi-bluetooth\"\u003eESP32 Dev Board\u003c\/a\u003e\u003c\/li\u003e\n    \u003cli\u003e\u003ca href=\"\/products\/elecrow-24inch-esp32-solo-miner-lcd-display\"\u003e2.4in TFT ILI9341\u003c\/a\u003e\u003c\/li\u003e\n    \u003cli\u003e\n\u003ca href=\"\/products\/tactile-button-pack-10x-6mm-switches-with-colored-caps-compoden\"\u003eTactile Button\u003c\/a\u003e x2\u003c\/li\u003e\n    \u003cli\u003e\n\u003ca href=\"\/products\/ntc-thermistor-temperature-sensor-module-3-pin-10k%CF%89\"\u003e10kΩ Potentiometer\u003c\/a\u003e x2\u003c\/li\u003e\n    \u003cli\u003e\n\u003ca href=\"\/products\/capacitor-variety-pack-6-values-100nf-to-470uf-30-pieces\"\u003e100nF Caps\u003c\/a\u003e x5\u003c\/li\u003e\n    \u003cli\u003e\n\u003ca href=\"\/products\/esp-wroom-32-breakout-board-pcb-55x52mm\"\u003ePCB Prototype Board\u003c\/a\u003e x2\u003c\/li\u003e\n    \u003cli\u003e\u003ca href=\"\/products\/4-channel-relay-board-for-esp32-30-pin-5v-control\"\u003e5V 2A PSU\u003c\/a\u003e\u003c\/li\u003e\n    \u003cli\u003e\u003ca href=\"\/products\/enclosure-box-for-diy-electronics-projects-compoden\"\u003eEnclosure Box\u003c\/a\u003e\u003c\/li\u003e\n    \u003cli\u003e\u003ca href=\"\/products\/soldering-kit-25w-with-solder-wire-flux-paste-compoden\"\u003eSoldering Iron\u003c\/a\u003e\u003c\/li\u003e\n    \u003cli\u003e\u003ca href=\"\/products\/soldering-kit-25w-with-solder-wire-flux-paste-compoden\"\u003eSolder Wire\u003c\/a\u003e\u003c\/li\u003e\n  \u003c\/ul\u003e\n\u003c\/div\u003e\n\n\u003cscript type=\"application\/ld+json\"\u003e\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [\n    {\n      \"@type\": \"Question\",\n      \"name\": \"What is included in the 4D Phase Space Trajectory Kit with ESP32?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"The 4D Phase Space Trajectory Kit with ESP32 includes all components needed: ESP32 Dev Board, 2.4in TFT ILI9341, Tactile Button, 10kΩ Potentiometer, 100nF Caps and more. Everything is pre-tested for compatibility and shipped from Bengaluru, India.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"What skill level is required for the 4D Phase Space Trajectory Kit with ESP32?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"This kit is designed for Advanced level makers, suitable for ages 21-24. Lorenz attractor computed on ESP32 and rendered as animated 3D projection on TFT with colour time axis. Estimated build time is 6-8 hrs.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"Can I buy the 4D Phase Space Trajectory Kit with ESP32 online in India?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Yes, the 4D Phase Space Trajectory Kit with ESP32 is available online at Compoden (compoden.in), India's AI-powered electronics and robotics store. Ships from Bengaluru in 1-5 business days across India.\"\n      }\n    }\n  ]\n}\n\u003c\/script\u003e\n\n\u003cscript type=\"application\/ld+json\"\u003e\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"Product\",\n  \"name\": \"4D Phase Space Trajectory Kit with ESP32\",\n  \"description\": \"Lorenz attractor computed on ESP32 and rendered as animated 3D projection on TFT with colour time axis.\",\n  \"sku\": \"CDN-KIT-2078\",\n  \"brand\": {\"@type\": \"Brand\", \"name\": \"Compoden\"},\n  \"offers\": {\n    \"@type\": \"Offer\",\n    \"url\": \"https:\/\/compoden.in\/products\/kit-4d-phase-space-trajectory\",\n    \"priceCurrency\": \"INR\",\n    \"price\": \"4455\",\n    \"availability\": \"https:\/\/schema.org\/InStock\",\n    \"seller\": {\"@type\": \"Organization\", \"name\": \"Compoden\"}\n  },\n  \"category\": \"Data \u0026 Visualization\"\n}\n\u003c\/script\u003e\u003cp\u003e\u003cstrong\u003eChoose your assembly option:\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eSoldering Kit\u003c\/strong\u003e — 25W soldering iron, 60\/40 solder wire, flux, and small perfboard for permanent assembly.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eBreadboard Combo\u003c\/strong\u003e — 800-point full-size breadboard with 65-piece jumper wire pack for solderless prototyping.\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Compoden","offers":[{"title":"Soldering Kit","offer_id":53469312516461,"sku":"CDN-KIT-2078-SLD","price":3880.0,"currency_code":"INR","in_stock":true},{"title":"Breadboard Combo","offer_id":53469312549229,"sku":"CDN-KIT-2078-BB","price":3350.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0999\/3997\/5533\/files\/kit-4d-phase-space-trajectory.png?v=1781947665","url":"https:\/\/compoden.com\/products\/kit-4d-phase-space-trajectory","provider":"Compoden","version":"1.0","type":"link"}