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So what is Mathematical Design? How can you make art using a desmos calculator?
In this short timeline, I will show you my journey of the process in creating a mathematical art design.

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During this entire process, I've had done a lot of researching and experimenting using the Desmos calculator to create several of my art pieces. As I progressed through, I've gained some knowledge and helpful tips in starting out my art pieces.

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When starting my Mathematical Design projects, my mind was completely blank. It was a rocky road at first but as I progressed, I soon learned that I can accomplished this and that things isn't as hard as it seemed.

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During this early process, I was interested in experimenting on different shapes and forms that I can create using this Diamond. This piece wasn't very exciting or fun to work on. Later on, you can see that this first draft never had much progression because I've abandoned it at the early stage as I focused on my other art pieces.

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While experimenting on this piece, I became fond of the twirling form. I wanted to make a cool swirly rainbow pattern and it end up look like this. As I look back at this piece, this remind me of the patterns from the skittles package.

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When I was creating this piece, I was experimenting on how I can create a heart inside of a sphere. After experimenting different ways to make a sphere, I became fond of the patterns on this sphere because it looks like a flower. So, I decided to keep it like that.

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So while I was researching on what formulas of what I can use. I came across and interesting art piece that caught my eyes. Supposing, this piece looked like a architectural structure, however the more I looked at it, the more it resembles the Eifel Tower.

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So, for this special art piece, I was inspired of making a sunflower, but because of my lack of knowledge ... it's just a complete mess.

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When things just doesn't turn out the way you want, you just want to spit fire on everything.

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For this draft I've learned to use the colors to overlay on another so it can create a illusion of a flower.
Then, I created a created a sphere and added patterns to it to make it seem like a sunflower seed.
Lastly, I pinpoint the origin of the circle and create a line between the flower, as I created the stalk and the leaves.

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So for Draft 5, it did not turn out the way that I hoped, and because I was a bit lazy on making every single petals on the sunflower pieces I somehow end up discovering a way to cover it up. Thus, as I further experiment on this particular piece. I managed to reach my original goal for this piece which was to create a sunflower.

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I was unsatisfied with draft 1.0 stalk and leaves because it looked very unsettling. So, once again I've done more researching and coding, which took approximately five hours. During this process, I inserted more than thirty lines on each of the leaves to make it look like a actual leaf. Though the left leaf took much more longer compared to the right leaf because it was much larger. In the end, I was very satisfied with the results.

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For the finishing touches, I changed the design patterns on the sunflower seed, as I finalized my desmos art for project 1.

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It was a rocky start and for me it took me a much longer time to create the art pieces for the reason of my lack of experience of how I can use the functions to my advantages. However, in the end I managed to grasp several concept as I discover more ways to create art.

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From what I've learned from Project 1, I've gained more knowledge then before. Throughout this whole process I was able to experiment on more things that I wasn't able to experiment before. There was a much more wider range of possibilities now that I know how to use some parabola functions given to me.

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This was a curve which I was very intrigued by before I started to develop more ideas for Project 2. When I saw this unusual curve, this reminded me of a bell. In the end, I tried overlapping the curves making it seem like a rainbow.

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This draft was a continuation of Draft 2. Before starting, I wanted to re-use the drafts I've created in Project 1, and I was glad that I did. In this draft I've learned to
change the colors of the background. I was able to experiment more of the size of each curves as I go on.

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This is the final product from Draft 2 and Rain yarn draft. So for this piece, I tried to challenge myself on how many curves I can create in this piece. From what you can tell by looking at this image, A LOT. In the end, this art piece looked seemed as if  the curves were spiraling down to a certain point creating a tiny yarn ball in the middle. If one was to pay a much more close attention to this piece, you start to realize that a few of the rainbow pattern seems much more brighter and bolder compared to other rainbow patterns. The reason is because I overlay it with another rainbow pattern thus creating a illusion as if some patterns appear to be more brighter and some appear to be fade in the background.

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This piece was my 2nd most advance piece compared to my first Project piece, which was the sunflower. However, this piece didn't required that many functions compared to my sunflower piece. As you can see, this is also another continuation of one of my previous drafts, Draft 3. For this final piece I managed to create a really cool looking stained-glass design as the background of the image. In this art piece I've enlarged the sphere and the heart. As seen in this image, the heart is transparent, so you can see the stained glassed design background. Surrounding the heart is a sphere with a design that looks a lot like a flower. If you look a little more closely there is a orange gradient spiral line going towards the heart, that is not very obvious to the eyes.

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Once again, this art piece is also another continuation from my other drafts from project 1, Draft 4. When I was working on this piece I wanted to experiment how I can play with the gradation of that one particular color. As seen in this piece the top of the tower seems much more lighter compared to the bottom of the tower. I've managed to create this gradation by using the patterns to my advantage, as you can see some of the patterns appears to be darker than the others. Thus, making it seem like a Night Tower.

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As you can see, this is the same Tower as the Night Tower however for this piece I was experimenting on the colors and gradation. I thought that the orange and the purple blended in very well together as if it was creating a sunset or perhaps a sunrise scenario. Similarly to the Night Tower the top of the tower colors seems to be much lighter compared to the bottom of the tower.

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For this experimental piece, I managed to create a checker like board with a object sitting in the middle. You may assume that it looks like a pillar sitting on what seems like a sofa. However, in my eyes that pillar seems more like a apple which had been eaten to the core. For the background I managed to mix the colors till I got the color that's currently displayed.

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In this piece, this was my attempt in changing the color schemes for Draft 6. I managed to make the checker like board, making it seems like a checker/chess piece that's in the middle of the image. I've learned overlay the colors on top of one another creating a really cool image.

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When I was creating this draft, I've had the most difficult time on figuring out how I can make the shapes of the butterfly look more unique and unusual. That was not until I came up with the idea to use color palettes that weren't already there. For this artwork I was experimenting on both the colors and the shape. In the end I went along with this color scheme and shape because it looks like a flower and a butterfly.

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This is a rotating sunflower, and while it's rotating it looks like a radiating sun.

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This is a heart that explodes fireworks. I really like the design of the background because it looks very similar to stained glass.

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This is a rotating yarn, as you look closely most of the colors of the strings are constantly being rotated around.

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This is a piece which the image is constantly overlayed creating those checker like patterns and object.

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This is a flapping drunk butterfly. When this butterfly flap it's wings it looks like it's dancing. I managed to make this butterfly flap by constantly rotating the object making it seem as if it's flying.

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This was a very rocky journey for me. I've managed to complete a lot of my deadlines for this semester and I've learned a lot from using the Desmos graphing calculator to create art. At first, I never knew that it's possible to make art using a graphing calculator. I am glad that I am able to express my creative side in math, which is usual something that I don't do very often. Overall, I've managed to gain a new skill and some experience in creating art using the Desmos graphing calculator.