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These 5 drafts are what I created before making my Final Draft 

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These 5 drafts are what I created before making my Final Draft 

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Although I felt all drafts were good, I felt that I could build off of Draft 4 the most. This led to me developing the draft in depth and incorporated my ideas of a half bright and half dull spirals together in a cohesive manner. 

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Although I felt all drafts were good, I felt that I could build off of Draft 4 the most. This led to me developing the draft in depth and incorporated my ideas of a half bright and half dull spirals together in a cohesive manner. 

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The vibrant and dull color palettes (below) inspired my final project because I wanted to make a piece of art that had half vibrant spirals and half dull spirals with a sense of division in the middle. 

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The vibrant and dull color palettes (below) inspired my final project because I wanted to make a piece of art that had half vibrant spirals and half dull spirals with a sense of division in the middle. 

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These are my 5 drafts of Project 2 before making my Final Draft 

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These are my 5 drafts of Project 2 before making my Final Draft 

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When deciding on which draft to develop further it was clear to me that Draft 1 was the right one to pick. Not to mention it felt like the one draft that could be made into a piece of art closest to the image that inspired me. 

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When deciding on which draft to develop further it was clear to me that Draft 1 was the right one to pick. Not to mention it felt like the one draft that could be made into a piece of art closest to the image that inspired me. 

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Below are examples of some of my favorite parent functions 

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Below are examples of some of my favorite parent functions 

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f(x)=x, or y=x

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f(x)=x^2, or y=x^2

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f(x)=|x|, or y=|x|

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f(x)=cos(x), or y=cos(x)

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Parametric functions used to create the displayed shapes below (circle, spiral, star). Both parametric equations for each image differ from one another which is how the shapes are different.

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This is one of my favorite images created by a parametric function that I've found on google. I like how it starts off as star-like in the middle then expands to the point it hits the circle that surrounds it.

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The principles of art, many of which I used in both my projects such as balance, pattern, unity, proportion, and repetition.

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The elements of art which were also used in both my projects. With those elements being line, shape, space, and color.

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1) Line
2) Shape
3) Form
4) Space
5) Value & Contrast
6) Color
7) Texture

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1. Line

There are many different types of lines, all characterized by their length being greater than their width. Lines can be static or dynamic depending on how the artist chooses to use them. They help determine the motion, direction and energy in a work of art. We see line all around us in our daily lives; telephone wires, tree branches, jet contrails and winding roads are just a few examples. Look at the photograph below to see how line is part of natural and constructed environments.

In this image of a lightning storm we can see many different lines. Certainly the jagged, meandering lines of the lightning itself dominate the image, followed by the straight lines of the skyline structures and the coast line. There are more subtle lines too, like the lights along the buildings. Lines are even implied by the reflections in the water.

The Nazca lines in the arid coastal plains of Peru date to nearly 500 BCE were scratched into the rocky soil, depicting animals on an incredible scale, so large that they are best viewed from the air. Let's look at how the different kinds of line are made.

Diego Velazquez's Las Meninas from 1656, ostensibly a portrait of the Infanta Margarita, the daughter of King Philip IV and Queen Mariana of Spain, offers a sumptuous amount of artistic genius; its sheer size (almost ten feet square), painterly style of naturalism, lighting effects, and the enigmatic figures placed throughout the canvas-including the artist himself -is one of the great paintings in western art history. Let's examine it (below) to uncover how Velazquez uses basic elements and principles of art to achieve such a masterpiece.

Actual lines are those that are physically present. The edge of the wooden stretcher bar at the left of Las Meninas is an actual line, as are the picture frames in the background and the linear decorative elements on some of the figures' dresses. How many other actual lines can you find in the painting?

Implied lines are those created by visually connecting two or more areas together. The gaze to the Infanta Margarita-the blonde central figure in the composition-from the meninas, or maids of honor, to the left and right of her, are implied lines. They visually connect the figures. By visually connecting the space between the heads of all the figures in the painting we have a sense of jagged implied line that keeps the lower part of the composition in motion, balanced against the darker, more static upper areas of the painting. Implied lines can also be created when two areas of different colors or tones come together. Can you identify more implied lines in the painting? Where? Implied lines are found in three-dimensional artworks, too. The sculpture of the Laocoon below, a figure from Greek and Roman mythology, is, along with his sons, being strangled by sea snakes sent by the goddess Athena as wrath against his warnings to the Trojans not to accept the Trojan horse. The sculpture sets implied lines in motion as the figures writhe in agony against the snakes.

Straight or classic lines provide structure to a composition. They can be oriented to the horizontal, vertical, or diagonal axis of a surface. Straight lines are by nature visually stable, while still giving direction to a composition. In Las Meninas, you can see them in the canvas supports on the left, the wall supports and doorways on the right, and in the background in matrices on the wall spaces between the framed pictures. Moreover, the small horizontal lines created in the stair edges in the background help anchor the entire visual design of the painting. Vertical and horizontal straight lines provide the most stable compositions. Diagonal straight lines are usually more visually dynamic, unstable, and tension-filled.

Expressive lines are curved, adding an organic, more dynamic character to a work of art. Expressive lines are often rounded and follow undetermined paths. In Las Meninas you can see them in the aprons on the girls' dresses and in the dog's folded hind leg and coat pattern. Look again at the Laocoon to see expressive lines in the figures' flailing limbs and the sinuous form of the snakes. Indeed, the sculpture seems to be made up of nothing but expressive lines, shapes and forms.

There are other kinds of line that encompass the characteristics of those above yet, taken together, help create additional artistic elements and richer, more varied compositions. Refer to the images and examples below to become familiar with these types of line.

Outline, or contour line is the simplest of these. They create a path around the edge of a shape. In fact, outlines often define shapes.

Hatch lines are repeated at short intervals in generally one direction. They give shading and visual texture to the surface of an object.

Crosshatch lines provide additional tone and texture. They can be oriented in any direction. Multiple layers of crosshatch lines can give rich and varied shading to objects by manipulating the pressure of the drawing tool to create a large range of values.

Line quality is that sense of character embedded in the way a line presents itself. Certain lines have qualities that distinguish them from others. Hard-edged, jagged lines have a staccato visual movement while organic, flowing lines create a more comfortable feeling. Meandering lines can be either geometric or expressive, and you can see in the examples how their indeterminate paths animate a surface to different degrees.

Although line as a visual element generally plays a supporting role in visual art, there are wonderful examples in which line carries a strong cultural significance as the primary subject matter.

Calligraphic lines use quickness and gesture, more akin to paint strokes, to imbue an artwork with a fluid, lyrical character. To see this unique line quality, look up the work of Chinese poet and artist Dong Qichang, dating from the Ming dynasty (1555-1637). A more geometric example from the Koran, created in the Arabic calligraphic style, dates from the 9 th century.

Both these examples show how artists use line as both a form of writing and a visual art form. American artist Mark Tobey (1890-1976) was influenced by Oriental calligraphy, adapting its form to the act of pure painting within a modern abstract style described as white writing.

2. Shape

A shape is defined as an enclosed area in two dimensions. By definition shapes are always flat, but the combination of shapes, color, and other means can make shapes appear three-dimensional, as forms. Shapes can be created in many ways, the simplest by enclosing an area with an outline. They can also be made by surrounding an area with other shapes or the placement of different textures next to each other-for instance, the shape of an island surrounded by water. Because they are more complex than lines, shapes are usually more important in the arrangement of compositions. The examples below give us an idea of how shapes are made.

Referring back to Velazquez's Las Meninas, it is fundamentally an arrangement of shapes; organic and hard-edged, light, dark and mid-toned, that solidifies the composition within the larger shape of the canvas. Looking at it this way, we can view any work of art, whether two or three-dimensional, realistic, abstract or non-objective, in terms of shapes alone.

Geometric Shapes vs. Organic Shapes

Shapes can be further categorized into geometric and organic. Examples of geometric shapes are the ones we can recognize and name: squares, triangles, circles, hexagons, etc. Organic shapes are those that are based on organic or living things or are more free form: the shape of a tree, face, monkey, cloud, etc.

3. Form

Form is sometimes used to describe a shape that has an implied third dimension. In other words, an artist may try to make parts of a flat image appear three-dimensional. Notice in the drawing below how the artist makes the different shapes appear three-dimensional through the use of shading. It's a flat image but appears three-dimensional.

This image is free of copyright restrictions.

When an image is incredibly realistic in terms of its forms (as well as color, space, etc.) such as this painting by Edwaert Collier, we call that trompe l'oeil, French for "fool the eye."

Edweart Collier, Trompe l'oeil with Writing Materials,

oil on canvas, c. 1702.

This image is in the public domain.

4. Space

Space is the empty area surrounding or between real or implied objects. Humans categorize space: there is outer space, that limitless void we enter beyond our sky; inner space, which resides in people's minds and imaginations, and personal space, the important but intangible area that surrounds each individual and which is violated if someone else gets too close. Pictorial space is flat, and the digital realm resides in cyberspace. Art responds to all of these kinds of space.

Many artists are as concerned with space in their works as they are with, say, color or form. There are many ways for the artist to present ideas of space. Remember that many cultures traditionally use pictorial space as a window to view realistic subject matter through, and through the subject matter they present ideas, narratives and symbolic content. The innovation of linear perspective, an implied geometric pictorial construct dating from fifteenth-century Europe, affords us the accurate illusion of three-dimensional space on a flat surface, and appears to recede into the distance through the use of a horizon line and vanishing point(s). You can see how one-point linear perspective is set up in the examples below:

One-point perspective occurs when the receding lines appear to converge at a single point on the horizon and used when the flat front of an object is facing the viewer. Note: Perspective can be used to show the relative size and recession into space of any object, but is most effective with hard-edged three-dimensional objects such as buildings.

A classic Renaissance artwork using one point perspective is Leonardo da Vinci's The Last Supper from 1498. Da Vinci composes the work by locating the vanishing point directly behind the head of Christ, thus drawing the viewer's attention to the center. His arms mirror the receding wall lines, and, if we follow them as lines, would converge at the same vanishing point.

Two-point perspective occurs when the vertical edge of a cube is facing the viewer, exposing two sides that recede into the distance, one to each vanishing point.

View Gustave Caillebotte's Paris Street, Rainy Weather from 1877 to see how two-point perspective is used to give an accurate view to an urban scene. The artist's composition, however, is more complex than just his use of perspective. The figures are deliberately placed to direct the viewer's eye from the front right of the picture to the building's front edge on the left, which, like a ship's bow, acts as a cleaver to plunge both sides toward the horizon. In the midst of this visual recession a lamp post stands firmly in the middle to arrest our gaze from going right out the back of the painting. Caillebotte includes the little metal arm at the top right of the post to direct us again along a horizontal path, now keeping us from traveling off the top of the canvas. As relatively spare as the left side of the work is, the artist crams the right side with hard-edged and organic shapes and forms in a complex play of positive and negative space.

The perspective system is a cultural convention well suited to a traditional western European idea of the "truth," that is, an accurate, clear rendition of observed reality. Even after the invention of linear perspective, many cultures traditionally use a flatter pictorial space, relying on overlapping, size differences, or vertical placement of components in a two-dimensional work of art. Examine the miniature painting of the Third Court of the Topkapi Palace from fourteenth-century Turkey to contrast its pictorial space with that of linear perspective. It's composed from a number of different vantage points (as opposed to vanishing points), all very flat to the picture plane. While the overall image is seen from above, the figures and trees appear as cutouts, seeming to float in mid air. Notice the towers on the far left and right are sideways to the picture plane. The trees and people occupying the upper parts of the image are meant to be perceived as further from the viewer as compared to those trees, buildings and people located near the bottom of the painting. This is an example of vertical placement.

As "incorrect" as it looks, the painting does give a detailed description of the landscape and structures on the palace grounds.

After nearly five hundred years using linear perspective, western ideas about how space is depicted accurately in two dimensions went through a revolution at the beginning of the 20 th century. A young Spanish artist, Pablo Picasso, moved to Paris, then western culture's capital of art, and largely reinvented pictorial space with the invention of Cubism, ushered in dramatically by his painting Les Demoiselles d'Avignon in 1907. He was influenced in part by the chiseled forms, angular surfaces and disproportion of African sculpture (refer back to the Male Figure from Cameroon) and mask-like faces of early Iberian artworks. For more information about this important painting, listen to the following question and answer.

In the early 20th century, Picasso, his friend Georges Braque and a handful of other artists struggled to develop a new space that relied on, ironically, the flatness of the picture plane to carry and animate traditional subject matter including figures, still life and landscape. Cubist pictures, and eventually sculptures, became amalgams of different points of view, light sources and planar constructs. It was as if they were presenting their subject matter in many ways at once, all the while shifting foreground, middle ground and background so the viewer is not sure where one starts and the other ends. In an interview, the artist explained cubism this way: "The problem is now to pass, to go around the object, and give a plastic expression to the result. All of this is my struggle to break with the two-dimensional aspect*"(from Alexander Liberman, An Artist in His Studio, 1960, page 113). Public and critical reaction to cubism was understandably negative, but the artists' experiments with spatial relationships reverberated with others and became - along with new ways of using color - a driving force in the development of a modern art movement that based itself on the flatness of the picture plane. Instead of a window to look into, the flat surface becomes a ground on which to construct formal arrangements of shapes, colors and compositions. For another perspective on this idea, refer back to module one's discussion of 'abstraction'.

You can see the radical changes cubism made in George Braque's landscape La Roche Guyon from 1909. The trees, houses, castle and surrounding rocks comprise almost a single complex form, stair-stepping up the canvas to mimic the distant hill at the top, all of it struggling upwards and leaning to the right within a shallow pictorial space.

As the cubist style developed, its forms became even flatter. Juan Gris's The Sunblind from 1914 splays the still life it represents across the canvas. Collage elements like newspaper reinforce pictorial flatness.

It's not so difficult to understand the importance of this new idea of space when placed in the context of comparable advances in science surrounding the turn of the nineteenth century. The Wright Brothers took to the air with powered flight in 1903, the same year Marie Curie won the first of two Nobel prizes for her pioneering work in radiation. Sigmund Freud's new ideas on the inner spaces of the mind and its effect on behavior were published in 1902, and Albert Einstein's calculations on relativity, the idea that space and time are intertwined, first appeared in 1905. Each of these discoveries added to human understanding and realligned the way we look at ourselves and our world. Indeed, Picasso, speaking of his struggle to define cubism, said "Even Einstein did not know it either! The condition of discovery is outside ourselves; but the terrifying thing is that despite all this, we can only find what we know" (from Picasso on Art, A Selection of Views by Dore Ashton, (Souchere, 1960, page 15).

Three-dimensional space doesn't undergo this fundamental transformation. It remains a visual and actual relationship between positive and negative spaces.

5. Value and Contrast

Value (or tone) is the relative lightness or darkness of a shape in relation to another. The value scale, bounded on one end by pure white and on the other by black, and in between a series of progressively darker shades of grey, gives an artist the tools to make these transformations. The value scale below shows the standard variations in tones. Values near the lighter end of the spectrum are termed high-keyed, those on the darker end are low-keyed.

In two dimensions, the use of value gives a shape the illusion of form or mass and lends an entire composition a sense of light and shadow. The two examples below show the effect value has on changing a shape to a form.

This same technique brings to life what begins as a simple line drawing of a young man's head in Michelangelo's Head of a Youth and a Right Hand from 1508. Shading is created with line (refer to our discussion of line earlier in this module) or tones created with a pencil. Artists vary the tones by the amount of resistance they use between the pencil and the paper they're drawing on. A drawing pencil's leads vary in hardness, each one giving a different tone than another. Washes of ink or color create values determined by the amount of water the medium is dissolved into.

The use of high contrast, placing lighter areas of value against much darker ones, creates a dramatic effect, while low contrast gives more subtle results. These differences in effect are evident in 'Guiditta and Oloferne' by the Italian painter Caravaggio, and Robert Adams' photograph Untitled, Denver from 1970-74. Caravaggio uses a high contrast palette to an already dramatic scene to increase the visual tension for the viewer, while Adams deliberately makes use of low contrast to underscore the drabness of the landscape surrounding the figure on the bicycle.

6. Color

Color is the most complex artistic element because of the combinations and variations inherent in its use. Humans respond to color combinations differently, and artists study and use color in part to give desired direction to their work.

Color is fundamental to many forms of art. Its relevance, use and function in a given work depend on the medium of that work. While some concepts dealing with color are broadly applicable across media, others are not.

The full of colors is contained in white light. Humans perceive colors from the light reflected off objects. A red object, for example, looks red because it reflects the red part of the spectrum. It would be a different color under a different light. Color theory first appeared in the 17 th century when English mathematician and scientist Sir Isaac Newton discovered that white light could be divided into a spectrum by passing it through a prism.

The study of color in art and design often starts with color theory. Color theory splits up colors into three categories: primary, secondary, and tertiary.

The basic tool used is a color wheel, developed by Isaac Newton in 1666. A more complex model known as the color tree, created by Albert Munsell, shows the spectrum made up of sets of tints and shades on connected planes.

There are a number of approaches to organizing colors into meaningful relationships. Most systems differ in structure only.

Traditional Model

Traditional color theory is a qualitative attempt to organize colors and their relationships. It is based on Newton's color wheel, and continues to be the most common system used by artists.

Traditional color theory uses the same principles as subtractive color mixing (see below) but prefers different primary colors.

The primary colors are red, blue, and yellow. You find them equidistant from each other on the color wheel. These are the "elemental" colors; not produced by mixing any other colors, and all other colors are derived from some combination of these three.

The secondary colors are orange (mix of red and yellow), green (mix of blue and yellow), and violet (mix of blue and red).

The tertiary colors are obtained by mixing one primary color and one secondary color. Depending on amount of color used, different hues can be obtained such as red-orange or yellow-green. Neutral colors (browns and grays) can be mixed using the three primary colors together.

White and black lie outside of these categories. They are used to lighten or darken a color. A lighter color (made by adding white to it) is called a , while a darker color (made by adding black) is called a .

Color Mixing

Think about color as the result of light reflecting off a surface. Understood in this way, color can be represented as a ratio of amounts of primary color mixed together. Color is produced when parts of the external light source's spectrum are absorbed by the material and not reflected back to the viewer's eye. For example, a painter brushes blue paint onto a canvas. The chemical composition of the paint allows all of the colors in the spectrum to be absorbed except blue, which is reflected from the paint's surface. Common applications of subtractive color theory are used in the visual arts, color printing and processing photographic positives and negatives.

The primary colors are red, yellow, and blue.

The secondary colors are orange, green and violet.

The tertiary colors are created by mixing a primary with a secondary color.

Black is mixed using the three primary colors, while white represents the absence of all colors. Note: because of impurities in subtractive color, a true black is impossible to create through the mixture of primaries. Because of this the result is closer to brown. Similar to additive color theory, lightness and darkness of a color is determined by its intensity and density.

Color Attributes

There are many attributes to color. Each one has an effect on how we perceive it.

Hue refers to color itself, but also to the variations of a color.

(as discussed previously) refers to the relative lightness or darkness of one color next to another. The value of a color can make a difference in how it is perceived. A color on a dark background will appear lighter, while that same color on a light background will appear darker.

Saturation refers to the purity and intensity of a color. The primaries are the most intense and pure, but diminish as they are mixed to form other colors. The creation of tints and shades also diminish a color's saturation. Two colors work strongest together when they share the same intensity.

Color Interactions

Beyond creating a mixing hierarchy, color theory also provides tools for understanding how colors work together.

Monochrome

The simplest color interaction is monochrome. This is the use of variations of a single hue. The advantage of using a monochromatic color scheme is that you get a high level of unity throughout the artwork because all the tones relate to one another. See this in Mark Tansey's Derrida Queries de Man from 1990.

Analogous Color

Analogous colors are similar to one another. As their name implies, analogous colors can be found next to one another on any 12-part color wheel:

You can see the effect of analogous colors in Paul Cezanne's oil painting Auvers Panoromic View

Color Temperature

Colors are perceived to have temperatures associated with them. The color wheel is divided into and colors. Warm colors range from yellow to red, while cool colors range from yellow-green to violet. You can achieve complex results using just a few colors when you pair them in warm and cool sets.

Complementary Colors

Complementary colors are found directly opposite one another on a color wheel. Here are some examples:

Blue and orange are complements. When placed near each other, complements create a visual tension. This color scheme is desirable when a dramatic effect is needed using only two colors.

7. Texture

At the most basic level, Three-dimensional works of art (sculpture, pottery, textiles, metalwork, etc.) and architecture have actual texture which is often determined by the material that was used to create it: wood, stone, bronze, clay, etc. Two-dimensional works of art like paintings, drawings, and prints may try to show implied texture through the use of lines, colors, or other ways. When a painting has a lot of actual texture from the application of thick paint, we call that impasto.

The first image below is a sculpture, and like all three-dimensional objects it has actual texture.

The next two images are details from the painting The Arnolfini Portrait by Jan van Eyck. Here, the artist has created implied texture. If you were to touch this painting you would not feel the fabric of the clothing and carpet, the wooden floor or the smooth metal of the chandelier, but our eyes "see" the texture.

Licenses and Attributions

CC licensed content, Shared previously

All rights reserved content

Teens talk about Picasso's Les Demoiselles d'Avignon, MoMA. License: All Rights Reserved. License terms: Standard YouTube License

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There are many different types of lines, all characterized by their length being greater than their width. Lines can be static or dynamic depending on how the artist chooses to use them. They help determine the motion, direction and energy in a work of art.

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All of the Desmos lessons throughout the year that helped better my understanding in their specific areas.

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A Desmos lesson on Trigonometric graphing. How to find the range of a function and how to find a function from a given range.

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A Desmos lesson on patterns and finding the certain rules needed to move an object to a certain spot, in a certain way.

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About the half-way point of the linear interpolation 

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About the half-way point of the linear interpolation 

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Below is the the Desmos notebook that holds the code for this linear interpolation. 

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Below is the the Desmos notebook that holds the code for this linear interpolation. 

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These are the two base functions for the Rotation Transformation shown 

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These are the two base functions for the Rotation Transformation shown 

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The base function for the vertical line resulted in the rotation transformation shown 

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The base function for the vertical line resulted in the rotation transformation shown 

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The base function for the horizontal line resulted in the rotation transformation shown 

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The base function for the horizontal line resulted in the rotation transformation shown 

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The combination of both rotation transformations led to the creation of this star-like image below. This image was used in my final draft of project 2 as well. 

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The combination of both rotation transformations led to the creation of this star-like image below. This image was used in my final draft of project 2 as well. 

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Below is the Desmos notebook for this rotation transformation so the code could be seen for how it was made. 

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Below is the Desmos notebook for this rotation transformation so the code could be seen for how it was made. 

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When thinking about what to create for this project I was watching the SCIHD channel and a show about space was on. The episode went in depth about black holes and that is where my inspiration came from. I wanted to create a black hole like background that would be "absorbing" the colorful planet-like circles. 

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When thinking about what to create for this project I was watching the SCIHD channel and a show about space was on. The episode went in depth about black holes and that is where my inspiration came from. I wanted to create a black hole like background that would be "absorbing" the colorful planet-like circles. 

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Some of the possible transformations to apply to functions. All of these transformations were used at some point in class and in my projects as well.

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A vertical translation upwards of 3 units is applied to the parent function of f(x)=x. This results in f(x)=x+3

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A horizontal compression of 5 is applied with a vertical translation downward by 4. This turns the parent function of f(x)=x^2 to f(x)=5x^2-4.

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I've always liked math but my last 2 years of high school started to change that. Math began to become boring to me, in large part due to me not learning anything for the entirety of two years. What was once my favorite subject became one of my least favorite, that was until this year. Taking this class helped me appreciate and start to like math again. I not only learned more in these past couple of months than the past couple of years but I also got to use the math I learned to code artwork of my desire. This class is directly responsible for me starting to appreciate math again and wanting to get back into mathematical stuff.

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Entering this semester I lacked in many areas of mathematics. It was so bad that I couldn't even tell you anything at all about parametric equations/functions and I definitely never heard of linear interpolation either. As the semester went on I began to remember all the previous things that may have slipped my mind, such as vectors. Vectors may not be the hardest of topics but I did relearn everything about them this year like how they always have a direction. Then towards the end of the semester I began to learn what parametric functions are, what their graphs look like, and what variable is present in its equations. I always thought that parametric equations were almost exactly like normal functions such as f(x)=x, but little did I know there's a lot more to them. Parametric functions consist of two parametric equations (one for x, and one for y) with its variable as "t" and only ever t, and they can create graphs vastly similar to those of linear functions or vastly different. As a whole I would say that my progression as a mathematician was a huge one as I now know various things I didn't when entering the class and I know how to apply them and explain them when needed.

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Last year, in my senior year I took a computer science class and learned to do basic coding for the first time in Python. With that being said heading into the semester I had a small bit of previous knowledge in the field of coding/programming. I knew how to do basic things such as changing code to move something the direction I wanted it to go or to dilate something. One thing I never learned was color codes, what their values did, and how to use those color codes on a website. In this class we learned a little bit about the Hex Values for the color code which is displayed as #FF0000 and is the same thing seen on the Color Palette website that I used from my first 2 projects but this interested me so I wanted to further look into color codes. I found that color codes have a number for R(Red), G(Green), and B(Blue) with the number ranging from 0-255. The higher the number is in one specific area meant more of that one colors was being used to create the color you're going for, for instance a solid green would be R-0, G-255, B-0. To apply these values to something on the webpage you're on you'd click fn-F12 (On a macbook) and then go to the subtitle console and write out the code needed with the number code being involved as well. This is how I changed my color scheme on Demsos for both projects to my liking. Although we didn't directly learn all about color codes in this class it was being shown the color palette website and how to change the colors on Desmos which sparked my interest to learn about this and know for the future. My progression as a programmer was a big one due to learning how to change a color scheme by applying code in the "Console" area of the websites code, I learned about the RGB values for color codes, and I learned how to directly use math equations and functions in programming to create images.

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My progression as an artist is in large part due to the fact that it was created through coding. Throughout my life I've always done artwork by hand, but in freshman year of high school I took a graphic designing class. The graphic design class primarily focused on photo shopping pictures, drawing custom logos on the computer, or making websites. That was the first real progression I've had as an artist up until this year. I've never used math or coding to make art before so the fact that this class was a mathematical design class it helped me expand as an artist in areas I never knew could create art. I had never even assumed that you could code something with math to create a piece of art but now that I do I'm going to continue to use this skill in the future. Not only did I come across a new way to create art, but I even came across a new style to my art through this course. The mathematical functions I would use (such as cosine or sine) created various curved lines that I typically would've never used, and helped me create very symmetrical and cohesive art.

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All of the listed column headings displayed are what I felt to be the most important parts to the class and the things that mattered most to the course. Everything outside of the projects and my own progress are all used throughout the course and were used by me in my two projects as well.

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At the beginning of the semester this basic function was just about the best I could do on Desmos when trying to program.

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As the semester progressed my ability and understanding of how to code progressed as well. This led me to create something as simple as the above parent function into something much more complex and unique such as the image below (draft 5 of project 1).

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This was one the first piece of artwork I ever created on Desmos in the class. I found it to be a very simplistic design but also one that was very put together and actually one of my favorite pieces of art I've created as well.

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This was the last piece of artwork I created for the class and I feel the difference my first piece is a huge one. I grew as an artist by making my art a lot more complex with more things going on rather than less. My first image was created mainly by straight lines and a square, the second image consists of various more things such as functions that appear to create circles, squares, and spiral like boxes. My artwork has become a lot more full, with more negative space in my pieces, and with the inclusion of more colors.

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In the beginning of the semester this was one of the best things I could create with math. Simplistic math equations/functions were the best I could do until further learning and re-learning all the math I previously knew.

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My skills as a mathematician grew exponentially from the beginning of the year as I could now create more complex functions/equations while also using lists as well. On top of this I learned what to put as the domain for parametric functions to get it to me liking.