Arduino Mega LCD TFT 320x480 Mandelbrot

26.09.2017

The Mandelbrot set is the set of complex numbers c for which the function ............

more teory here: https://en.wikipedia.org/wiki/Mandelbrot_set

or here: https://mathworld.wolfram.com/MandelbrotSet.html

Used:

3.5 inch TFT LCD touch screen Module for Arduino mega2560 for US $13.49 :

https://www.ebay.com/itm/3-5-inch-TFT-LCD-touch-screen-Module-for-Arduino-mega2560-mega-2560-r3-/162102438173?epid=506781222&hash=item25be0ee91d:g:oD0AAOSwB-1Yt8xt

Arduino mega - clone

Code:

Below is procedure to calculate and view mandelbrot set on LCD display. Procedure has 7 parameters.

x0,y0,y1,x1 - start and stop coordinate in mandelbrot set

sx,sy -size of generated picture in pixels

lim - limit number of iteration that are used to compute each pixel. higher limit = better quality = more time

void LCD::mandelbrot(float x0,float y0,float x1, float y1,int16_t sx, int16_t sy,uint16_t lim ){
    int16_t limit,counter1,i,j;
    float cr,ci,zr,zi;
    limit=lim;
    setRectangle(0,0,sx-1,sy-1);
    LCD_Write_COM(RAMWR);

    float di,dr; //size of delta 
    float sqzr;  //square Zr
    float sqzi;  //square Zi
    di=(y1-y0)/sx;  // calculate delta as size/pixel
    //dr=(x1-x0)/sy;
    dr=di;
    cr=x0;   //CR
    for (i=0;i<sy;i++)
    {
        cr=cr+dr;
        ci=y0;
        for (j=0;j<sx;j++)
        {
            ci=ci+di;
            zr=0.0;
            zi=0.0;
            sqzr=zr*zr;
            sqzi=zi*zi;
            counter1=0; 
            do {//calculate each pixel
                zi=zr*zi;
                zi+=zi;
                zi+=ci;
                zr=sqzr-sqzi+cr;
                sqzr = zr*zr;
                sqzi = zi*zi;
                ++counter1;     
                
            } while ((counter1<=limit) && ((sqzr+sqzi)<=4.0) );
            
            //pixel color transformation
            uint16_t col = counter1<<5; //GREEN
        //  uint16_t col = (counter1>>1)<<11; //RED
        //  uint16_t col = (counter1>>1); //BLUE
            if (counter1>63) col=63<<5;   //optimalization1 - soft edges
            if (counter1>=limit) setPixel(BLACK); else setPixel(col); //show pixel
        }
    }
}

Update1: coloring

code for nice colors

           ////pixel color transformation
            //uint16_t col = counter1<<5; //GREEN
            ////    uint16_t col = (counter1>>1)<<11; //RED
            ////    uint16_t col = (counter1>>1); //BLUE
            //if (counter1>63) col=63<<5;   //optimalization1 - soft edges
            //if (counter1>=limit) setPixel(BLACK); else setPixel(col); //show pixel
            uint16_t fi=255*counter1/limit;
            uint8_t cb,cg,cr;
            
            if ((fi>=0)&&(fi<32)) {cb=fi;cr=0;cg=0;}
            if ((fi>=32)&&(fi<64)) {cg=fi-32;cr=0;cb=31;}
            if ((fi>=64)&&(fi<96)) {cb=95-fi;cg=31;cr=0;}
            if ((fi>=96)&&(fi<128)) {cr=fi-96;cg=31;cb=0;}
            if ((fi>=128)&&(fi<160)) {cg=159-fi;cr=31;cb=0;}
            if ((fi>=160)&&(fi<192)) {cb=fi-160;cg=0;cr=31;}
            if ((fi>=192)&&(fi<224)) {cg=fi-192;cr=31,cb=31;}
            if ((fi>=224)&&(fi<256)) {cr=255-fi;cg=31;cb=31;}
            
            
            
            uint16_t pc= (((cb<<3)&0b11111000)>>3)|(((cg<<3)&0b11111000)<<3)|(((cr<<3)&0b11111000)<<8);
            if (counter1>=limit) setPixel(BLACK); else setPixel(pc);

Gallery

Download Atmel Studio 7.0 Project

LCD35_mandelbrot_v0.zip