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Learning About Parent Functions:
In this daily question of September 16th, I explored what happens when I combine multiple parent functions by addition and/or multiplication. As a programmer, I learned that, by combining 2 graphs together, you can get an image that resembles the two of them and see their correlation.
https://www.desmos.com/calculator/yec0mnwqkr

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I was playing with absolute values to see what I could create. It led me to creating cool strikes. You can tell that I used absolute value, because the graph creates v shapes!
https://www.desmos.com/calculator/7nplcgzpie

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At that time, I was unsure on what to focus on for my first project, so I started with creating a human face...I tried.
https://www.desmos.com/calculator/3tnm9iwwfu

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This was when I found the polar function by accident. Not knowing what it was, I started playing with it to see what it would create. After that, I combined other parent functions to get the final product.
https://www.desmos.com/calculator/plwe7lokqn

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This was the coolest mistake I have ever made while trying to create art with math functions. I named the file "Texture" on Desmos because I can see a rough texture while looking at this picture. Using tan, sin and cos I was able to create this beautiful mistake.

https://www.desmos.com/calculator/e1drdlvysi

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As the final draft, I had an image in my head, which was a nature scene that included people in it. However, while working on the final piece, I came up with this image instead. It reminded me of the ocean, and you'll see where I went from there on the next slide!

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Through my 5th draft, I was able to create this project. I used sin/cos functions to create the birds, water, and the seaweed. For the dolphin, I combined parent functions together.
https://www.desmos.com/calculator/y4e3fxrjh3

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October 14th- Daily Question: Favorite curve.
My favorite curve for the campuswire homework was
A cardioid. The word comes from the Greek work καρδία , which means "heart". I did not know much about Cardioid graphs, through research and this desmos experience, I learned that it's a plane curve that is traced by a point on the perimeter of a circle.
https://www.desmos.com/calculator/1oun2cbvl7

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This was my first time trying to graph a parametric function. I did not have any expectations as to what kind of shapes it would create, but it was cool how it's a combination of two functions creating 1 image.
https://www.desmos.com/calculator/avqrnabdad

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October 26- Daily Question:  Favorite exploration of rotated parametric function

By using the equation f(x)=x cos(h) and then adding a slider to it, I was able to come up with a function that rotates. On desmos by clicking on the triangle sign, or dragging the slider, you can see the function move.
https://www.desmos.com/calculator/wpu8zb75bj

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Since this was my first draft, I didn't have any particular image in my head that I wanted to create, so I started experimenting with parametric functions. It first didn't satisfy me to get the design, so I got the same equations, but reflected them to make it look like a reflection.
https://www.desmos.com/calculator/r8lh9u1wxp

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For my 2nd draft of project #2, I created this flower using some polar function, and some basic parametric functions such as r=b sin (v theta). Since there was a variable, I started dragging the slides to see what kind of flower shapes it would give me. I decided to stay with this one (picture above).
https://www.desmos.com/calculator/mfukimvsja

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After I did my 2nd draft, I had a plan in mind, that I would do some floral work for this project. So just like the last one, I decided to go with creating flowers. However, on this one the only functions I used are polar functions.
https://www.desmos.com/calculator/2ambnztjyw

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This draft was a combination of some parent functions, polar and parametric functions. I started with creating the red flower like design in the middle with the equation (a(cos t- cos 4t), a ((-sin t-sin (7t))). After, I used similar equation but only covered the half of the red flower to create a different tone. Since that did not feel like enough for this draft, I decided to create some cosine curve on both sides. and in the middle. I concluded this draft by adding a basic circle in the middle of the flower like design.
https://www.desmos.com/calculator/84osg2ufhk

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For some reason, I wanted to do a heartbeat and put a heart in the middle using cardioid equation for my final draft. Anyhow I made a mistake and came up with the snail design instead, so I decided to keep it. The equation that gave me the heartbeat is y=(sin(x)2sin(6x))

https://www.desmos.com/calculator/atpnzq47qk

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Combining formulas from my previous drafts and the knowledge that I gained from this class, I was able to create this beautiful mandala artwork.
I started by creating the flowers in the middle using polar functions. For example, one of them is r=T sin( J theta ). By creating more of those and adding variables to them which allowed me to change the shape and size, I created the flowers. After, I added the squares on 4 sides using transformed parametric functions. I say transformed, because I overlapped them and changed the values to change their position by little, as well as add a few more lines.
Since this project was on parametric functions, I added extra parametric equations to add on to the mandala art. I concluded it by adding a parent function using "tan" so that it can create a background for the mandala. For the final step, I change the color and made everything pastel to match the art.
https://www.desmos.com/calculator/ogqmbgbdqz