Newton-Raphson equation

fractal {
	// Set region margins and declare state vector as [x,n] where x and n are built-in variables
	orbit [<-1.5,-1.5>,<1.5,1.5>] [x,n] {
		begin {
			s = 0;
			if (~julia) {
				x = w;
				w = 1;
			}
		}
		loop [0, 200] (s = 1) {
			ta = x * x;
			tb = x * ta;
			tc = tb - w;
			if (mod2(tc) < 0.0000001) {
				x = x - w;
				stop;
			}
			tc = 2 * tb + w;
			td = 3 * ta;
			if (mod2(td) < 0.000000000000000000000001) {
				td = <0.000000000001, 0>;
			}
			x = tc / td;
		}
	}
	// Set background color to alpha=1, red=1, green=1, blue=1
	color [(1,0,0,0)] {
		// Create palette with 200 colors and name gradient
		palette gradient {
			[#FFFF0000 > #FFFFFFFF, 15];
			[#FFFFFFFF > #FFFFFFFF, 185];
		}
		// Apply rule when n > 0 and set opacity to 1.0
		rule (n > 0) [1] {
			// Set color to element n - 1 of gradient (gradient has 200 colors starting from index 0)
			gradient[n - 1]
		}
	}
}

Newton-Raphson equation


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