Fibonacci128 HDR 86mm

Posted March 29, 2024

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Details

Fibonacci128 HDR is a beautiful 86mm circular disc with 128 SK9822-EC20 HDR RGB LEDs surface mounted in a Fibonacci distribution. Swirling and pulsing like a colorful galaxy, it’s mesmerizing to watch.

It consists of 128 RGB LEDs, arranged into a circular Fermat’s spiral pattern.

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In disc phyllotaxis, as in the sunflower and daisy, the mesh of spirals occurs in Fibonacci numbers because divergence (angle of succession in a single spiral arrangement) approaches the golden ratio. The shape of the spirals depends on the growth of the elements generated sequentially. In mature-disc phyllotaxis, when all the elements are the same size, the shape of the spirals is that of Fermat spirals—ideally. That is because Fermat's spiral traverses equal annuli in equal turns. The full model proposed by H Vogel in 1979[2] is

r = c \sqrt{n},
\theta = n \times 137.508^\circ,

where θ is the angle, r is the radius or distance from the center, and n is the index number of the floret and c is a constant scaling factor. The angle 137.508° is the golden angle which is approximated by ratios of Fibonacci numbers.[3]

Fermat's spiral. (2015, October 24). In Wikipedia, The Free Encyclopedia. Retrieved 02:45, February 24, 2016, from https://en.wikipedia.org/w/index.php?title=Fermat%27s_spiral

Specifications

  • Size: 3.39 x 3.39 x .063 inch (86 x 86 x 1.6 mm)
  • 2 layer printed circuit board
  • FR4 substrate
  • Black SMOBC (solder mask over bare copper)
  • HASL (Hot Air Solder Leveling) Finish
  • Designed in the US by Evil Genius Labs

FastLED Maps

const uint8_t  physicalToFibonacci[NUM_LEDS] { 0, 21, 42, 63, 84, 105, 126, 113, 92, 71, 50, 29, 8, 16, 37, 58, 79, 100, 121, 108, 87, 66, 45, 24, 3, 11, 32, 53, 74, 95, 116, 124, 103, 82, 61, 40, 19, 6, 27, 48, 69, 90, 111, 119, 98, 77, 56, 35, 14, 1, 22, 43, 64, 85, 106, 127, 114, 93, 72, 51, 30, 9, 17, 38, 59, 80, 101, 122, 109, 88, 67, 46, 25, 4, 12, 33, 54, 75, 96, 117, 125, 104, 83, 62, 41, 20, 7, 28, 49, 70, 91, 112, 120, 99, 78, 57, 36, 15, 2, 23, 44, 65, 86, 107, 115, 94, 73, 52, 31, 10, 18, 39, 60, 81, 102, 123, 110, 89, 68, 47, 26, 5, 13, 34, 55, 76, 97, 118 };
const uint8_t  fibonacciToPhysical[NUM_LEDS] { 0, 49, 98, 24, 73, 121, 37, 86, 12, 61, 109, 25, 74, 122, 48, 97, 13, 62, 110, 36, 85, 1, 50, 99, 23, 72, 120, 38, 87, 11, 60, 108, 26, 75, 123, 47, 96, 14, 63, 111, 35, 84, 2, 51, 100, 22, 71, 119, 39, 88, 10, 59, 107, 27, 76, 124, 46, 95, 15, 64, 112, 34, 83, 3, 52, 101, 21, 70, 118, 40, 89, 9, 58, 106, 28, 77, 125, 45, 94, 16, 65, 113, 33, 82, 4, 53, 102, 20, 69, 117, 41, 90, 8, 57, 105, 29, 78, 126, 44, 93, 17, 66, 114, 32, 81, 5, 54, 103, 19, 68, 116, 42, 91, 7, 56, 104, 30, 79, 127, 43, 92, 18, 67, 115, 31, 80, 6, 55 };

byte coordsX[NUM_LEDS] = { 137, 181, 201, 213, 219, 221, 218, 193, 198, 199, 195, 184, 160, 164, 176, 178, 175, 167, 154, 127, 142, 152, 158, 157, 142, 140, 140, 132, 119, 103, 85, 45, 65, 84, 101, 116, 126, 121, 106, 89, 70, 51, 32, 9, 25, 43, 63, 83, 104, 118, 84, 62, 42, 25, 11, 0, 11, 19, 32, 47, 68, 96, 81, 58, 43, 33, 27, 26, 49, 47, 50, 58, 74, 105, 94, 77, 70, 69, 74, 83, 125, 110, 99, 91, 90, 96, 114, 108, 112, 121, 135, 152, 193, 174, 156, 141, 129, 123, 130, 141, 155, 172, 191, 210, 239, 221, 202, 182, 164, 145, 164, 186, 206, 225, 241, 255, 248, 237, 222, 204, 182, 151, 170, 196, 214, 227, 236, 241 };
byte coordsY[NUM_LEDS] = { 130, 137, 150, 166, 184, 204, 224, 235, 216, 197, 178, 159, 141, 160, 182, 203, 222, 240, 255, 251, 237, 221, 202, 180, 147, 167, 195, 215, 229, 240, 247, 227, 228, 225, 216, 202, 181, 158, 186, 199, 206, 207, 203, 166, 177, 184, 185, 181, 166, 139, 161, 165, 161, 152, 139, 122, 96, 114, 129, 140, 146, 143, 132, 123, 110, 93, 74, 55, 39, 59, 78, 96, 112, 126, 109, 89, 69, 49, 30, 13, 0, 13, 28, 46, 67, 90, 102, 72, 50, 33, 19, 9, 21, 24, 31, 43, 60, 85, 112, 75, 57, 47, 42, 42, 74, 66, 63, 66, 75, 96, 95, 86, 85, 91, 101, 115, 142, 126, 114, 106, 105, 115, 121, 124, 134, 148, 166, 185 };
byte angles[NUM_LEDS] = { 136, 134, 139, 145, 150, 155, 161, 169, 164, 159, 154, 148, 143, 157, 162, 167, 172, 178, 183, 192, 186, 181, 176, 171, 165, 179, 184, 189, 195, 200, 205, 220, 214, 209, 203, 198, 193, 201, 206, 212, 217, 223, 228, 242, 237, 231, 226, 220, 214, 221, 229, 234, 240, 246, 251, 2, 11, 5, 255, 249, 243, 237, 252, 3, 8, 14, 20, 25, 34, 29, 23, 17, 12, 4, 21, 26, 32, 38, 43, 49, 63, 57, 52, 47, 41, 35, 44, 50, 56, 61, 66, 72, 86, 81, 75, 70, 64, 59, 69, 74, 78, 84, 89, 95, 109, 104, 98, 93, 88, 84, 97, 102, 107, 113, 118, 123, 132, 127, 121, 116, 111, 107, 121, 125, 130, 136, 141, 146 };
byte radius[NUM_LEDS] = { 18, 104, 148, 180, 207, 233, 255, 243, 218, 192, 162, 124, 67, 93, 140, 175, 204, 230, 251, 238, 213, 186, 155, 115, 46, 79, 132, 169, 196, 222, 245, 250, 229, 206, 178, 145, 103, 60, 120, 157, 188, 214, 236, 242, 221, 197, 168, 135, 87, 29, 107, 147, 179, 205, 228, 248, 235, 213, 186, 159, 121, 68, 91, 136, 168, 196, 222, 243, 231, 206, 180, 149, 109, 45, 75, 124, 160, 191, 217, 239, 248, 226, 202, 174, 139, 96, 57, 115, 154, 185, 212, 235, 243, 220, 196, 167, 132, 84, 31, 106, 147, 179, 207, 230, 239, 217, 191, 159, 124, 70, 95, 139, 173, 201, 225, 247, 234, 211, 184, 153, 114, 51, 83, 132, 167, 196, 222, 245 };

Pixelblaze Map

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