Fog of war with alpha cut off as white color

Simple black fog with noise map and white color cut off as alpha. First screenshot is example, second is for nose and third is for texture.

Shader code

shader_type canvas_item;
render_mode blend_mix;

uniform sampler2D NOISE_PATTERN : repeat_enable;

// Amount of detail.
uniform int octaves = 4;

// Opacity of the output fog.
uniform float starting_amplitude: hint_range(0.0, 0.5) = 0.5;

// Rate of pattern within the fog.
uniform float starting_frequency = 1.0;

// Shift towards transparency (clamped) for sparser fog.
uniform float shift: hint_range(-1.0, 0.0) = 0.0;

// White cut off
uniform float white_cutoff: hint_range(0.0, 1.0) = 0.999;

// Direction and speed of travel.
uniform vec2 velocity = vec2(1.0, 1.0);

// Color of the fog.
uniform vec4 fog_color = vec4(0.0, 0.0, 0.0, 1.0);

float rand(vec2 uv) {
	float amplitude = starting_amplitude;
	float frequency = starting_frequency;
	float output = 0.0;
	for (int i = 0; i < octaves; i++) {
		output += texture(NOISE_PATTERN, uv * frequency).x * amplitude;
		amplitude /= 2.0;
		frequency *= 2.0;
	}
	return clamp(output + shift, 0.0, 1.0);
}

void fragment() {
	vec4 mainTexture = texture(TEXTURE, UV);
	vec2 motion = vec2(rand(UV + TIME * starting_frequency * velocity));
	vec4 negative_fog_value = vec4(1.0 - fog_color.rgb, fog_color.a);
	vec4 color = mix(mainTexture, fog_color, rand(UV + motion));
	COLOR = color;
	float real_alfa_cutoff = 1.0 - white_cutoff;
	if(color.r * color.g * color.b > real_alfa_cutoff)
	{
	    COLOR.a = 0.0;
	}
	
}

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