diff --git a/manimlib/shaders/newton_fractal/frag.glsl b/manimlib/shaders/newton_fractal/frag.glsl
index 8315f9ec..223f8556 100644
--- a/manimlib/shaders/newton_fractal/frag.glsl
+++ b/manimlib/shaders/newton_fractal/frag.glsl
@@ -75,7 +75,7 @@ vec2 seek_root(vec2 z, vec2[MAX_DEGREE + 1] coefs, int max_steps, out float n_it
         }
         z = z - step;
     }
-    n_iters -= clamp((threshold - curr_len) / (last_len - curr_len), 0.0, 1.0);
+    n_iters -= log(curr_len) / log(threshold);
 
     return z;
 }
@@ -118,7 +118,7 @@ void main() {
             color = colors[i];
         }
     }
-    color *= 1.0 + (0.01 * saturation_factor) * (n_iters - 5 * saturation_factor);
+    color *= 1.0 + (0.01 * saturation_factor) * (n_iters - 2 * saturation_factor);
 
     if(black_for_cycles > 0 && min_dist > CLOSE_ENOUGH){
         color = vec4(0.0, 0.0, 0.0, 1.0);