// G Edwards, gedwards2@gmail.com, 21 Feb 2020

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// Start at 7.30

// 8.30 - first recognizable Mandelbrot ! after about 200 errors

// 9.30 - got it tidy enough to publish

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let Width = 1000;    // size of drawing area

let Height = 750;

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let maxIter = 80;    // max steps to run the Mandelbrot iteration

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// Standard Processing / p5.js setup function. This is run once by the p5 framework.

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function setup() {

   createCanvas(Width, Height);

}

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// Standard p5.js drawing function. This is run repeatedly by the p5 framework.

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function draw() {

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   for(let i = 0; i < Width; i++) {            // loop over the columns of the canvas

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      let ci = 0.8 + (i - Width / 2)  / 400;   // i part of complex(i,j). The 0.8 shifts it to a good position.

      if(i%100 === 0) prt("column", i, ", x value", ci.toFixed(2));  // some feedback in console

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      for(let j = 0; j < Height; j++) {        // loop over rows of the canvas

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         let cj = (j - Height / 2) / 400;      // j part of complex(i,j)

         let result = iterate(ci, cj);

         if( result < maxIter) stroke(color(255));  // black

         else stroke(0);                            // white

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         point(i, j);                               // one pixel

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         // Check points are really 1 pixel

         // if((i % 10) === 0 && (j % 10) === 0) stroke(255,0,0), point(i, j);

      }

   }

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   prt("Done");

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   noLoop();                                    // stop the repetitive running of draw()

}

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// The key maths. We don't have a standard complex lib in JavaScript or p5.js, just do it by hand with the i, j values.

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function iterate(ci, cj) {

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   let zi = 0;   // Start the iteration with z = (0, 0).

   let zj = 0;

   let n = 0;

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   // while (complexAbs(zi, zj) <= 2 && n < maxIter) {  // Don't need this, sqrt is expensive, just test against the square

   while ( ((zi * zi) + (zj * zj) ) <= 4 && n < maxIter) {

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      let znew = product(zi, zj, zi, zj);

      zi = znew[0] - ci;

      zj = znew[1] - cj;

      n += 1;

   }

   return n;

}

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// Don't need to use this. Just test the square.

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function complexAbs(i, j) {

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   return sqrt(i * i + j * j);

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}

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// The old familiar complex product ! Learned this in about Year 11 or 12 high school.

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function product(i1, j1, i2, j2) {

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   let pi = (i1 * i1) - (j1 * j2);

   let pj = (i1 * j2) + (j2 * i1);

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   return [pi, pj];   // return an array

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}

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// Convenience interlude - console.log() is tedious to type.

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function prt(...args) {

   console.log(...args);

}

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