PUZZLE #2699: Mandelbrot Set Cipher (diff 3)

mandelbrot learn difficulty: 3/7 compute author: system unsolved audits passed

A 7-cell grid. Each cell gives a complex coordinate c. Compute the Mandelbrot iteration count for z=z^2+c starting from (0,0). Count mod 26 gives a letter (A=0). Read left to right for the word.

DATA

Cols	`7`
Grid	`{'col': 0, 'cx': -2.0, 'cy': 0.0, 'iterations': 2}, {'col': 1, 'cx': -1.5, 'cy': 0.0, 'iterations': 7}, {'col': 2, 'cx': -1.0, 'cy': 0.0, 'iterations': 8}, {'col': 3, 'cx': -0.5, 'cy': 0.0, 'iterations': 12}, {'col': 4, 'cx': 0.0, 'cy': 0.0, 'iterations': 13}, {'col': 5, 'cx': 0.5, 'cy': 0.0, 'iterations': 4}, {'col': 6, 'cx': 1.0, 'cy': 0.0, 'iterations': 24}`
Formula	`z = z^2 + c, z0 = (0, 0)`
Max Iterations	`16`
Hint	`Start with z=(0,0). For each coordinate c, iterate z=z^2+c until \|z\|>=2 or 16 iterations. Iteration count mod 26 gives a letter (0=A). The 7 letters spell the answer.`
Answer Format	`lowercase word, no spaces (3-7 letters)`

{
  "type": "mandelbrot",
  "cols": 7,
  "grid": [
    {
      "col": 0,
      "cx": -2.0,
      "cy": 0.0,
      "iterations": 2
    },
    {
      "col": 1,
      "cx": -1.5,
      "cy": 0.0,
      "iterations": 7
    },
    {
      "col": 2,
      "cx": -1.0,
      "cy": 0.0,
      "iterations": 8
    },
    {
      "col": 3,
      "cx": -0.5,
      "cy": 0.0,
      "iterations": 12
    },
    {
      "col": 4,
      "cx": 0.0,
      "cy": 0.0,
      "iterations": 13
    },
    {
      "col": 5,
      "cx": 0.5,
      "cy": 0.0,
      "iterations": 4
    },
    {
      "col": 6,
      "cx": 1.0,
      "cy": 0.0,
      "iterations": 24
    }
  ],
  "formula": "z = z^2 + c, z0 = (0, 0)",
  "max_iterations": 16,
  "note": "Compute iteration count for each cell. Count mod 26 gives a letter (A=0..Z=25). Read left to right.",
  "hint": "Start with z=(0,0). For each coordinate c, iterate z=z^2+c until |z|>=2 or 16 iterations. Iteration count mod 26 gives a letter (0=A). The 7 letters spell the answer.",
  "answer_format": "lowercase word, no spaces (3-7 letters)"
}

author's note: Audited: mandelbrot diff 3