diff --git a/cocos/core/curves/gradient.ts b/cocos/core/curves/gradient.ts
index 9ad938e15de..9d1b76ac11b 100644
--- a/cocos/core/curves/gradient.ts
+++ b/cocos/core/curves/gradient.ts
@@ -24,7 +24,7 @@
 
 import { CCClass } from '../data';
 import { Enum } from '../value-types';
-import { Color, lerp, repeat, EPSILON, approx } from '../math';
+import { Color, lerp, repeat, EPSILON, approx, random } from '../math';
 
 const Mode = Enum({
     Blend: 0,
@@ -172,8 +172,8 @@ export class Gradient {
      * @returns @en Randomized color. @zh 随机生成的颜色。
      */
     public getRandomColor (out: Color): Color {
-        const c = this.colorKeys[Math.trunc(Math.random() * this.colorKeys.length)];
-        const a = this.alphaKeys[Math.trunc(Math.random() * this.alphaKeys.length)];
+        const c = this.colorKeys[Math.trunc(random() * this.colorKeys.length)];
+        const a = this.alphaKeys[Math.trunc(random() * this.alphaKeys.length)];
         out.set(c.color);
         out._set_a_unsafe(a.alpha);
         return out;
diff --git a/cocos/core/math/utils.ts b/cocos/core/math/utils.ts
index 0af2c7d624a..3b653aba193 100644
--- a/cocos/core/math/utils.ts
+++ b/cocos/core/math/utils.ts
@@ -31,6 +31,8 @@ const _d2r = Math.PI / 180.0;
 
 const _r2d = 180.0 / Math.PI;
 
+let _random = Math.random;
+
 export const HALF_PI = Math.PI * 0.5;
 export const TWO_PI = Math.PI * 2.0;
 
@@ -121,7 +123,18 @@ export function toDegree (a: number): number {
 /**
  * @method random
  */
-export const random = Math.random;
+export function random (): number {
+    return _random();
+}
+
+/**
+ * @en Set a custom random number generator, default to Math.random
+ * @zh 设置自定义随机数生成器，默认为 Math.random
+ * @param func custom random number generator
+ */
+export function setRandGenerator<TFunction extends (...any) => number> (func: TFunction): void {
+    _random = func;
+}
 
 /**
  * @en Returns a floating-point random number between min (inclusive) and max (exclusive).<br/>
@@ -129,10 +142,10 @@ export const random = Math.random;
  * @method randomRange
  * @param min
  * @param max
- * @return The random number.
+ * @return {Number} The random number.
  */
 export function randomRange (min: number, max: number): number {
-    return Math.random() * (max - min) + min;
+    return random() * (max - min) + min;
 }
 
 /**
diff --git a/cocos/particle-2d/particle-simulator-2d.ts b/cocos/particle-2d/particle-simulator-2d.ts
index 2902322ea8a..96e68cf67b7 100644
--- a/cocos/particle-2d/particle-simulator-2d.ts
+++ b/cocos/particle-2d/particle-simulator-2d.ts
@@ -22,7 +22,7 @@
  THE SOFTWARE.
 */
 
-import { Vec2, Color, js, misc } from '../core';
+import { Vec2, Color, js, misc, random, IColorLike } from '../core';
 import { vfmtPosUvColor, getComponentPerVertex } from '../2d/renderer/vertex-format';
 import { PositionType, EmitterMode, START_SIZE_EQUAL_TO_END_SIZE, START_RADIUS_EQUAL_TO_END_RADIUS } from './define';
 import { ParticleSystem2D } from './particle-system-2d';
@@ -150,12 +150,12 @@ export class Simulator {
         // Init particle
         // timeToLive
         // no negative life. prevent division by 0
-        particle.timeToLive = psys.life + psys.lifeVar * (Math.random() - 0.5) * 2;
+        particle.timeToLive = psys.life + psys.lifeVar * (random() - 0.5) * 2;
         const timeToLive = particle.timeToLive = Math.max(0, particle.timeToLive);
 
         // position
-        particle.pos.x = psys.sourcePos.x + psys.posVar.x * (Math.random() - 0.5) * 2;
-        particle.pos.y = psys.sourcePos.y + psys.posVar.y * (Math.random() - 0.5) * 2;
+        particle.pos.x = psys.sourcePos.x + psys.posVar.x * (random() - 0.5) * 2;
+        particle.pos.y = psys.sourcePos.y + psys.posVar.y * (random() - 0.5) * 2;
 
         // Color
         let sr = 0;
@@ -167,30 +167,30 @@ export class Simulator {
         const endColor = psys.endColor;
         const endColorVar = psys.endColorVar;
 
-        particle.color.r = sr = misc.clampf(startColor.r + startColorVar.r * (Math.random() - 0.5) * 2, 0, 255);
-        particle.color.g = sg = misc.clampf(startColor.g + startColorVar.g * (Math.random() - 0.5) * 2, 0, 255);
-        particle.color.b = sb = misc.clampf(startColor.b + startColorVar.b * (Math.random() - 0.5) * 2, 0, 255);
-        particle.color.a = sa = misc.clampf(startColor.a + startColorVar.a * (Math.random() - 0.5) * 2, 0, 255);
-        particle.deltaColor.r = (misc.clampf(endColor.r + endColorVar.r * (Math.random() - 0.5) * 2, 0, 255) - sr) / timeToLive;
-        particle.deltaColor.g = (misc.clampf(endColor.g + endColorVar.g * (Math.random() - 0.5) * 2, 0, 255) - sg) / timeToLive;
-        particle.deltaColor.b = (misc.clampf(endColor.b + endColorVar.b * (Math.random() - 0.5) * 2, 0, 255) - sb) / timeToLive;
-        particle.deltaColor.a = (misc.clampf(endColor.a + endColorVar.a * (Math.random() - 0.5) * 2, 0, 255) - sa) / timeToLive;
+        particle.color.r = sr = misc.clampf(startColor.r + startColorVar.r * (random() - 0.5) * 2, 0, 255);
+        particle.color.g = sg = misc.clampf(startColor.g + startColorVar.g * (random() - 0.5) * 2, 0, 255);
+        particle.color.b = sb = misc.clampf(startColor.b + startColorVar.b * (random() - 0.5) * 2, 0, 255);
+        particle.color.a = sa = misc.clampf(startColor.a + startColorVar.a * (random() - 0.5) * 2, 0, 255);
+        particle.deltaColor.r = (misc.clampf(endColor.r + endColorVar.r * (random() - 0.5) * 2, 0, 255) - sr) / timeToLive;
+        particle.deltaColor.g = (misc.clampf(endColor.g + endColorVar.g * (random() - 0.5) * 2, 0, 255) - sg) / timeToLive;
+        particle.deltaColor.b = (misc.clampf(endColor.b + endColorVar.b * (random() - 0.5) * 2, 0, 255) - sb) / timeToLive;
+        particle.deltaColor.a = (misc.clampf(endColor.a + endColorVar.a * (random() - 0.5) * 2, 0, 255) - sa) / timeToLive;
 
         // size
-        let startS = psys.startSize + psys.startSizeVar * (Math.random() - 0.5) * 2;
+        let startS = psys.startSize + psys.startSizeVar * (random() - 0.5) * 2;
         startS = Math.max(0, startS); // No negative value
         particle.size = startS;
         if (psys.endSize === START_SIZE_EQUAL_TO_END_SIZE) {
             particle.deltaSize = 0;
         } else {
-            let endS = psys.endSize + psys.endSizeVar * (Math.random() - 0.5) * 2;
+            let endS = psys.endSize + psys.endSizeVar * (random() - 0.5) * 2;
             endS = Math.max(0, endS); // No negative values
             particle.deltaSize = (endS - startS) / timeToLive;
         }
 
         // rotation
-        const startA = psys.startSpin + psys.startSpinVar * (Math.random() - 0.5) * 2;
-        const endA = psys.endSpin + psys.endSpinVar * (Math.random() - 0.5) * 2;
+        const startA = psys.startSpin + psys.startSpinVar * (random() - 0.5) * 2;
+        const endA = psys.endSpin + psys.endSpinVar * (random() - 0.5) * 2;
         particle.rotation = startA;
         particle.deltaRotation = (endA - startA) / timeToLive;
 
@@ -202,18 +202,18 @@ export class Simulator {
         particle.aspectRatio = psys.aspectRatio || 1;
 
         // direction
-        const a = misc.degreesToRadians(psys.angle + this._worldRotation + psys.angleVar * (Math.random() - 0.5) * 2);
+        const a = misc.degreesToRadians(psys.angle + this._worldRotation + psys.angleVar * (random() - 0.5) * 2);
         // Mode Gravity: A
         if (psys.emitterMode === EmitterMode.GRAVITY) {
-            const s = psys.speed + psys.speedVar * (Math.random() - 0.5) * 2;
+            const s = psys.speed + psys.speedVar * (random() - 0.5) * 2;
             // direction
             particle.dir.x = Math.cos(a);
             particle.dir.y = Math.sin(a);
             particle.dir.multiplyScalar(s);
             // radial accel
-            particle.radialAccel = psys.radialAccel + psys.radialAccelVar * (Math.random() - 0.5) * 2;
+            particle.radialAccel = psys.radialAccel + psys.radialAccelVar * (random() - 0.5) * 2;
             // tangential accel
-            particle.tangentialAccel = psys.tangentialAccel + psys.tangentialAccelVar * (Math.random() - 0.5) * 2;
+            particle.tangentialAccel = psys.tangentialAccel + psys.tangentialAccelVar * (random() - 0.5) * 2;
             // rotation is dir
             if (psys.rotationIsDir) {
                 particle.rotation = -misc.radiansToDegrees(Math.atan2(particle.dir.y, particle.dir.x));
@@ -221,12 +221,12 @@ export class Simulator {
         } else {
             // Mode Radius: B
             // Set the default diameter of the particle from the source position
-            const startRadius = psys.startRadius + psys.startRadiusVar * (Math.random() - 0.5) * 2;
-            const endRadius = psys.endRadius + psys.endRadiusVar * (Math.random() - 0.5) * 2;
+            const startRadius = psys.startRadius + psys.startRadiusVar * (random() - 0.5) * 2;
+            const endRadius = psys.endRadius + psys.endRadiusVar * (random() - 0.5) * 2;
             particle.radius = startRadius;
             particle.deltaRadius = (psys.endRadius === START_RADIUS_EQUAL_TO_END_RADIUS) ? 0 : (endRadius - startRadius) / timeToLive;
             particle.angle = a;
-            particle.degreesPerSecond = misc.degreesToRadians(psys.rotatePerS + psys.rotatePerSVar * (Math.random() - 0.5) * 2);
+            particle.degreesPerSecond = misc.degreesToRadians(psys.rotatePerS + psys.rotatePerSVar * (random() - 0.5) * 2);
         }
     }
 
@@ -275,7 +275,7 @@ export class Simulator {
             const y1 = -halfHeight;
             const x2 = halfWidth;
             const y2 = halfHeight;
-            const rad = -misc.degreesToRadians(particle.rotation);
+            const rad = -misc.degreesToRadians(particle.rotation as number);
             const cr = Math.cos(rad);
             const sr = Math.sin(rad);
             // bl
@@ -313,13 +313,13 @@ export class Simulator {
             vbuf[offset + 29] = 0;
         }
         // color
-        Color.toArray(vbuf, particle.color, offset + 5);
-        Color.toArray(vbuf, particle.color, offset + 14);
-        Color.toArray(vbuf, particle.color, offset + 23);
-        Color.toArray(vbuf, particle.color, offset + 32);
+        Color.toArray(vbuf, particle.color as IColorLike, offset + 5);
+        Color.toArray(vbuf, particle.color as IColorLike, offset + 14);
+        Color.toArray(vbuf, particle.color as IColorLike, offset + 23);
+        Color.toArray(vbuf, particle.color as IColorLike, offset + 32);
     }
 
-    public step (dt): void {
+    public step (dt: number): void {
         const assembler = this.sys.assembler!;
         const psys = this.sys;
         const node = psys.node;
diff --git a/cocos/particle/animator/noise-module.ts b/cocos/particle/animator/noise-module.ts
index b4106e54f90..0eb677aed3f 100644
--- a/cocos/particle/animator/noise-module.ts
+++ b/cocos/particle/animator/noise-module.ts
@@ -22,7 +22,7 @@
  THE SOFTWARE.
 */
 
-import { CCFloat, CCInteger, _decorator, Vec3 } from '../../core';
+import { CCFloat, CCInteger, _decorator, Vec3, random } from '../../core';
 import { ParticleNoise } from '../noise';
 import { Particle, PARTICLE_MODULE_NAME, ParticleModuleBase } from '../particle';
 
@@ -302,12 +302,12 @@ export class NoiseModule extends ParticleModuleBase {
         this.noise.setOctaves(this.octaves, this.octaveMultiplier, this.octaveScale);
 
         this.samplePosition.set(particle.position);
-        this.samplePosition.add3f(Math.random() * 1.0, Math.random() * 1.0, Math.random() * 1.0);
+        this.samplePosition.add3f(random() * 1.0, random() * 1.0, random() * 1.0);
         this.noise.setSamplePoint(this.samplePosition);
         this.noise.getNoiseParticle();
 
         const noisePosition: Vec3 = this.noise.getResult();
-        noisePosition.multiply3f(Math.random(), Math.random(), Math.random());
+        noisePosition.multiply3f(random(), random(), random());
         Vec3.add(particle.position, particle.position, noisePosition.multiplyScalar(dt));
     }
 
diff --git a/cocos/particle/animator/texture-animation.ts b/cocos/particle/animator/texture-animation.ts
index a08dd4f5b05..fd15feccbc1 100644
--- a/cocos/particle/animator/texture-animation.ts
+++ b/cocos/particle/animator/texture-animation.ts
@@ -23,7 +23,7 @@
 */
 
 import { ccclass, tooltip, displayOrder, type, formerlySerializedAs, serializable, range } from 'cc.decorator';
-import { lerp, pseudoRandom, repeat, Enum } from '../../core';
+import { lerp, pseudoRandom, repeat, Enum, random, error } from '../../core';
 import { Particle, ParticleModuleBase, PARTICLE_MODULE_NAME } from '../particle';
 import CurveRange from './curve-range';
 import { ModuleRandSeed } from '../enum';
@@ -117,7 +117,7 @@ export default class TextureAnimationModule extends ParticleModuleBase {
 
     set mode (val) {
         if (val !== Mode.Grid) {
-            console.error('particle texture animation\'s sprites is not supported!');
+            error('particle texture animation\'s sprites is not supported!');
         }
     }
 
@@ -207,7 +207,7 @@ export default class TextureAnimationModule extends ParticleModuleBase {
     }
 
     set flipU (val) {
-        console.error('particle texture animation\'s flipU is not supported!');
+        error('particle texture animation\'s flipU is not supported!');
     }
 
     @serializable
@@ -218,7 +218,7 @@ export default class TextureAnimationModule extends ParticleModuleBase {
     }
 
     set flipV (val) {
-        console.error('particle texture animation\'s flipV is not supported!');
+        error('particle texture animation\'s flipV is not supported!');
     }
 
     @serializable
@@ -229,7 +229,7 @@ export default class TextureAnimationModule extends ParticleModuleBase {
     }
 
     set uvChannelMask (val) {
-        console.error('particle texture animation\'s uvChannelMask is not supported!');
+        error('particle texture animation\'s uvChannelMask is not supported!');
     }
 
     /**
@@ -263,7 +263,7 @@ export default class TextureAnimationModule extends ParticleModuleBase {
      * @internal
      */
     public init (p: Particle): void {
-        p.startRow = Math.floor(Math.random() * this.numTilesY);
+        p.startRow = Math.floor(random() * this.numTilesY);
     }
 
     /**