Golden Spiral Clock With Fibonacci Segments
A working clock face where a rotating second hand carries a golden spiral of fixed length from its center, sweeping past twelve fixed Fibonacci-curve segments arranged around the dial. As the hand passes each segment, it glows green then returns to white, linking uniform time intervals to the spiral's self-similar growth pattern. Useful for students exploring Fibonacci numbers, the golden ratio, logarithmic spirals, and how geometric growth can be mapped onto periodic motion like clock hands.
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The prompt that made it
Designing a The Most Mesmerizing Clock, Where time is visually tracked along a continuous movable golden spiral! This innovative mathematical visualization plots hours and minutes across curved intervals corresponding to Fibonacci numbers (1, 1, 2, 3, 5, 8, 13), creating a deeply satisfying and hypnotic loop of time passing. Some important designing instructions are 1) Clock dial is a circle have number from 1 to 12 2) clock have one second-hand which have circular movement faster then second and this hand associated with sufficient long golden spiral with constant length, when hand of clock move then spiral is also move because it is associated with its 3) Spiral starting point is the center of the clock 4) Outside the dial there must be 12 segments of curves impression of the same spiral which remain fix during the movement of spiral. These segment of spirals would same as uploded picture tjat os 6 curve segment are above the dial and have labels 1, 2, 3, 4, 5, & 6, and remaining 6 curve segments are below the dial and have numbers 7, 8, 9, 10, 11 & 12. Clock hand will move from 1 and at the same time spiral curve hide the segment curve above the dial which have the label 1 and segment colour cange from white to green(glowing) and after crossing this segment then colour again change back to its original white. When hand of clock moves to 2 then movable spiral hide the another segment curves which have label 2 and it is above the first curve segment and its colour change from white to radian green (glowing) and after crossing its, colour of segment again change back to its original white colour and so on, after crossing the spiral curve segment 6 its then spiral tail hide the curve segment 7 which is blow the dial and its colour change from white to green (glowing) and after crossing its, colour come back to its original white and spiral going to hide the segment 8 and so on. During whole process clock numbers are also displayed in digital form as in the uploaded image and continuously change during the movement like digital clock.
Make the next one in this series
- Show how the golden spiral relates to nested Fibonacci squares growing outward from the clock center
- Animate the golden ratio converging as consecutive Fibonacci numbers are divided in a side panel
- Compare this Fibonacci spiral clock to a standard Archimedean spiral clock to highlight growth rate differences
