Jason Cameron

Assignment 1

3 min read

wow | Desmos

For my functional art project, I created a tranquil landscape scene featuring clouds, a sun, grass, a flower, and stars. I used multiple parent functions and transformations to bring this scene to life.

The grass area was crafted using sine functions (y = sin(x)) with horizontal compressions, vertical shrinking, and vertical translations to create varied wave patterns that simulate different layers of grass. For the clouds, I employed quadratic functions (y = x²) with vertical reflections, horizontal and vertical translations, and vertical stretching to achieve their rounded appearance.

The sun was created using a circle function ((x-h)² + (y-k)² = r²) with rays constructed from linear functions (y = mx + b) with domain restrictions. The flower combines cubic functions (y = x³) and their variations with radical transformations, creating delicate petals and a stem.

One of my main challenges was achieving grass’s natural, flowing appearance. I overcame this by carefully adjusting the period of each sine wave and their vertical positions. Another challenge was creating the flower’s complex shape, which I solved by using domain restrictions and combining multiple versions of cubic functions to create the petals.

The design incorporates symmetry through the sun’s rays and the flower petals, adding visual balance to the composition.

Parent Functions and Transformations Used

Parent Functions:

  1. Linear function (y = x) - Used for sun rays

  2. Quadratic function (y = x²) - Used for clouds

  3. Cubic function (y = x³) - Used for flower petals

  4. Circle/conic section ((x-h)² + (y-k)² = r²) - Used for the sun

  5. Sine function (y = sin(x)) - Used for grass

  6. Absolute value function (y = |x|) - Used for flower stem

  7. Radical functions (y = √x) - Used for flower petals

Transformations:

  2. Vertical and horizontal translations (changing h and k values)

  3. Vertical and horizontal stretching/compression

  4. Reflections (negating functions)

  5. Domain restrictions (using inequality constraints)

  6. Function combinations (using multiple functions to create complex shapes)

All Functions used

Grass

Y < 0.5sin(x/2) - 1

Y < 0.4sin(x/1.8) - 1.4

Y < 0.3sin(x/2.2) - 1.8

Y < 0.2sin(x/1.5) - 2.2

Y < 0.1sin(x/2.5) - 2.6

Y < -2.8

Sun

(x-7)² + (y-5)² < 1.2

Y - 5 = 0.5(x-7) {7 > y > 5}

Y - 5 = -0.5(x-7) {7 > y > 5}

Y - 5 = 1.5(x-7) {8 > y > 5}

Y - 5 = -1.5(x-7) {2 < y < 5}

Clouds

Y < -0.1(x-0)² + 5 {y > 4}

Y < -0.1(x-2)² + 4.8 {y > 4}

Y < -0.1(x+2)² + 4.5 {y > 4}

Y > 0.1(x-0.3)² + 1.95 {y < 4}

Flower

Y = (x-4.4)³ + 1 {0.5 < y < 1.5}

Y = -(x-4.4)³ + 1 {0.5 < y < 1.5}

Y = -√((x-4.4)³) + 1 {0.5 < y < 1.5}

Y = -√(-(x-4.4)³) + 1 {0.5 < y < 1.5}

Y = √((x-4.4)³) + 1 {0.5 < y < 1.5}

Y = √(-(x-4.4)³) + 1 {0.5 < y < 1.5}

Y = 4|x-3.9| - {x > 4.015} {y < 1}

Stars (point functions)

(4,6)

(2,6)

(6,7)

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Graph View