Final Design

The program features two equations multiplied to create the z coordinate of the surface points. The first is the equation of the triangle wave which contains the a and p parameters, which is simply a cosine function that is multiplied by the x and y coordinates and contained within an inverse cosine function. The direction of the triangle wave can be adjusted using conditional statements, which creates the alternating pattern. The second is a sine function enveloping a square root of an equation that contains the x and y coordinates and the c and t parameters. This function creates the waves of irregular peaks, and by integer dividing the x and y values by t, a geometric, rocky surface is formed.

Variation Matrix 1

In this variation matrix, the parameters c and t are varied while parameters a, p are kept constant. By increasing parameter c and t, the number of sine waves radiating outwards are reduced. It can also be seen that the effects of varying parameter t on the sine waves are much greater than the effects of varying parameter c. Parameter t also controls the formation of the geometric surface. Increasing the t value will generate larger, but fewer indentations on the model’s surface. The models found to be most desirable contain the values c = 40 / t = 2, and c = 20 / t = 4.

Variation Matrix 2

In this variation matrix, the parameters a and p are varied while parameters c, t are kept constant. By increasing parameter a, the peaks increase in height and the troughs increase in depth. Increasing parameter p reduces the amount of triangle waves and causes the waves to be more spread out. The models found to be most desirable contain the values a = 9 / p = 15.8, and a = 9 / p = 23.5.

Desirability Matrix

To create this matrix, two criteria for desirability of the model were defined. The model must have degree of complexity, which is controlled by the p and t parameters; and the model must resemble a natural terrain, which is controlled by the a and c parameters. It was found that although increasing complexity creates more visually appealing structures, models too complex did not resemble the natural terrain of a mountainous region. The model found to be most desirable contains the values a = 9 / c = 10 / p = 15.8 / t = 4. The model found to be least desirable contains the values a = 1 / c = 70 / p = 23.5 / t = 6.

Design Evolution

Here are the various stages of the design and displays how the final model was generated. The parameters used in each model are shown as well. Earlier models have simpler grasshopper python codes, and thus may not be controlled by all four parameters used to create the final design.