# The digital art of the recurrence formula that I couldn't control.

## I couldn't control it. By chance as always...

I wrote a creative coding code with the 'Processing' programming language and it makes a very interesting digital art.

I tried to use my custom noise formula as an angle for calculating the coordinates in the recurrence formula. And I found it generates a very interesting pattern.

I used this custom noise formula in various artworks of mine.

Example artworks.

etc.

It's a very useful function in my creative coding. But I can't control to make a pattern that I want to even now.

## The 'Processing' example code.

This code does not display any images on the screen but just generates image files.

Please feel free to use this code under the terms of the GPL. To see other works based on my code is my pleasure. And my honor.

```/**
* Think it Over.
* Draw vector field with my custom noise formula.
*
* @author @deconbatch
* @version 0.1
* Processing 3.2.1
* 2019.05.25
*/

void setup() {

size(1080, 1080);
colorMode(HSB, 360, 100, 100, 100);
smooth();

}

void draw() {

int   ptnCntMax = 7; // draw 7 patterns
float hueInit   = random(360.0);

// shape parameters
float xPhase = random(1.0);
float yPhase = random(1.0);

translate(width * 0.5, height * 0.5);
background(0.0, 0.0, 90.0, 100);
noFill();

for (int ptnCnt = 0; ptnCnt < ptnCntMax; ++ptnCnt) {

float ptnRatio = map(ptnCnt, 0, ptnCntMax, 0.0, 1.0);

// pattern shape
int   plotCntMax = floor(random(5000.0, 10000.0));
float plotDiv    = random(0.002, 0.02);
// complexity
float complexity = random(0.5, 2.0);
// start point of calculation
float pStart     = random(1.0);

float baseHue = hueInit + map(ptnRatio * ptnRatio, 0.0, 1.0, 0.0, 120.0);
float baseSat = map(ptnRatio, 0.0, 1.0, 40.0, 20.0);
float baseBri = map(ptnRatio, 0.0, 1.0, 30.0, 50.0);
float baseAlp = 100.0;

// initial value of vector field calculation
float xPoint = pStart + cos(TWO_PI * (xPhase + ptnRatio));
float yPoint = pStart + sin(TWO_PI * (yPhase + ptnRatio));
float rPoint = 0.0;

// draw line with curveVertex()
strokeWeight(1.0);
stroke(baseHue % 360.0, baseSat, baseBri, baseAlp);
beginShape();
for (int plotCnt = 0; plotCnt < plotCntMax; ++plotCnt) {

float plotRatio = map(plotCnt, 0, plotCntMax, 0.0, 1.0);

float xPrev = xPoint;
float yPrev = yPoint;
float rPrev = rPoint;

// vector field calculation
rPoint += customNoise(TWO_PI * (xPrev + plotRatio) * complexity, TWO_PI * (yPrev * plotRatio) * complexity);
xPoint += plotDiv * cos(TWO_PI * rPoint) * plotRatio;
yPoint += plotDiv * sin(TWO_PI * rPoint) * plotRatio;

curveVertex((xPoint - pStart) * 0.25 * width, (yPoint - pStart) * 0.25 * height);

}
endShape();

}

casing();
saveFrame("frames/####.png");

if (frameCount >= 3) {
exit();
}

}

/**
* casing : draw fancy casing
*/
private void casing() {
rectMode(CENTER);
fill(0.0, 0.0, 0.0, 0.0);
strokeWeight(54.0);
stroke(0.0, 0.0, 60.0, 100.0);
rect(0.0, 0.0, width, height);
strokeWeight(50.0);
stroke(0.0, 0.0, 100.0, 100.0);
rect(0.0, 0.0, width, height);
noStroke();
noFill();
}

/**
* customNoise : returns -1.0 .. 1.0 almost random but interesting value
*/
float customNoise(float _x, float _y) {
return pow(sin(_x), 3) * cos(pow(_y, 2));
}

/*

This program is free software: you can redistribute it and/or modify
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <http://www.gnu.org/licenses/>
*/
```

No Comment