Mandelbrot set

A vector is a quantity that has both the magnitude as well as direction. The size of a vector is denoted by a scalar quantity which is considered as quantity that has only the magnitude but does not have direction. Vector quantities are mainly represented by an arrow that is drawn to scale and pointing to a specified direction.

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Fig 1 represents a vector whose magnitude is 20 meters heading in the direction of 030’

The vector represents displacement vectors with several features that are essential in an appropriate vector diagram. The vector diagram has a scalar quantity that is denoted by 20 meters labeled as‘d’. In addition, the arrow has an arrowhead that points into a specific direction 030’. The magnitude and direction of this vector is well defined. The vector is a displacement of 20 meters in the direction 030’. The direction of the vector is mainly expressed as an angle expressed in bearing about its tail.

There are three Newton’s Laws of motion. The first Newton law of motion is often regarded as the law of inertia. The law states that a body that is in a constant state of motion or rest remains in that state provided no external force acts on it. This is the law that causes passengers in a moving vehicle to be launched forward when a vehicle applies emergency brakes or passengers jerk backwards when a vehicle starts moving.

Newton’s second law of motion states that when an external force acts on a moving or a stationary body, the acceleration produced is inversely proportional to the mass of the body and directly proportion to the force applied and takes place in the direction of the force. The law is the one that is responsible for the acceleration or decelerations of the bodies.

Newton’s third law of motion states that for every action there is an equal and opposite reaction. For instance, when one step on the ground one exerts a certain force on the ground and in return the ground exerts an equal and opposite force on the feet. This is the law that is applied in determining the momentum of the bullet when it is fired from the gun.

The momentum of the bullet is determined by multiplying the mass of the gun with the recoil velocity of the gun which should be equal to the mass of the bullet multiplied by the speed of the bullet- which represents the momentum of the bullet. This is true due to the law of conservation of momentum which states that momentum before is equal to momentum after.

Mandelbrot set is a set of complex numbers. An image of complex numbers is plotted on a complex number plane. Before plotting the image, one first determines whether a given number is inside the set of number or not using the following formula. Z= z2+c where c is a constant, z starts from zero and changes with every test. After the test, the magnitude of z is then determined. If the magnitude of z is less than 2, the number is then inside the set and if greater than 2 the number is outside the Mandelbrot set.

After determining a several numbers as part of the Mandelbrot set they are plotted on the complex number plane to form an image. After forming the image, color may be added on those points that are not inside the set. The colors are used to make the image more conspicuous in order to make the regions of the Mandelbrot sets that are too small to be visible (Dewey, 1996).

Reference List

Dewey, D. (1996). Introduction to Mandelbrot Set. Retrieved 6 April 2012 from