Blog
Hi. My name is Jayden. I am a 7th grader living in the sunny San Francisco bay area, and I have been writing these posts since 3rd grade.
Notice: if you are looking for the intuition series posts, they were relocated to the Intuition Series tab.
Newton’s Fractal
3 November 2024
UI not included yet
Polynomial Division Calculator
31 July 2024
The front page is getting overwhelmed with all of the code, so to view the calculator, you have to click more.
I Found Primes
7 May 2024
Recently, I was thinking about finding a prime-finding algorithm. This eventually led to me basically rediscovering the Sieve of Eratosthenes algorithm.
Mass Spring Softbody Model
15 March 2024
To make an object, click the “make” button. Then, hover over the place you want to set the position of the object, and then click.
Spring Stiffness
Separation Between Nodes
Make Box:
Box Width
Box Height
Make Polygon:
Sides
Layers
This is my mass spring softbody model.
Each of the red dots is a node and each of the black lines is a spring. The node has a mass, so it is called the mass spring model.
In each timestep, the springs force some acceleration on the nodes. This is calculated with Hooke’s Law, which is \(F_s = -k \cdot s\), where \(k\) is displacement and \(s\) is spring stiffness.
This simulation is quite fun to play with. For more ideas to use this and more explanation, go here: Mass-Spring Model Video
New Music Genres, Scientifically
26 February 2024
My dad and I were talking in the car about “the creativity of people” and how they never seem to run out of new genres of music. I also had this thought before, so I decided to make this scientific.
I’m going to judge music types off of three things:
melody presence: how much melody is present
drum/beat presence: how much drum/beat is present
and lyrics: how much lyrics there are
Making an AI: Part 2
21 December 2023
I am still trying to write an AI.
The first part is here: Making an AI: Part 1.
Today, I actually wrote some code. I did it all on my own (which probably wasn’t the best idea).
Here, I’ll try to explain the idea behind the part that I wrote. If you are interested, I’ll explain my code bit by bit after.
Continued Fraction Calculator
24 October 2023
This is my continued fraction calculator.
| If you used the first ... numbers | Fraction | Value |
Enter values below as a list seperated by commas (ex. 1,4,23,2,5)
It might not work well when dealing with a very long list of numbers.
Solve for every first N numbers:
Try:
\(π\):
3,7,15,1,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,2,1,84,2,1
,1,15,3,13,1,4,2,6,6,99,1,2,2,6,3,5,1,1,6,8,1,7,1,2,3
,7,1,2,1,1,1,2,1,1,1,3,1,1,8,1,1,2,1,6,1,1,5,2,2,3,1,
2,4,4,16,1,161,45,1,22,1,2,2,1,4,1,2,24,1,2,1,3,1,2,1
and so on (without a pattern).
\(e\) (yes, there is a pattern):
2,1,2,1,1,4,1,1,6,1,1,8,1,1,10,...
\(\sqrt{2}\):
1,2,2,2,2,2,2,2,...
\(\phi\) (golden ratio):
1,1,1,1,1,1,1,1,1,1,...
Read on for a more detailed explanation of continued fractions.
Making an AI: Part 1
24 October 2023
I am trying to write an AI.
I wanted to just start programming, but my dad was a lot more sensible and recommended that I try to watch this guy, Andrej Karpathy, so that I could learn the basics. My dad then realized that I didn’t even know what dot products were, so I just kept watching the playlist, The Essence of Linear Algebra by 3Blue1Brown, which I had already started.
I probably know more than I need to about dot products to do this, because the main use for dot products in AI (from my limited knowledge of both subjects) is just multiplying a lot of stuff.
Didn’t do anything interesting yet.
Solar System and Three Body System Simulations
7 October 2023
I wrote a gravity simulation.
Here is a video that I made on simulating the solar system.
Here is a video that I made on the three body problem.
This is a brief overview of the code that I wrote:
Mandelbrot Set
22 September 2023
This post is about the Mandelbrot set. I also included a rendering of the Mandelbrot set , with zooming capabilities.
Accuracy (how many repetitions of checking)
Slime Mold Simulation
4 September 2023
WARNING: IF YOUR COMPUTER IS AN OLD POTATO LIKE MINE, DO NOT MAKE TOO MANY PIXELS OR AGENTS.
I made an interesting simulation of slime mold. First, the simulation creates a lot of agents. These agents each have a x position, a y position, and a direction, which points to one of the eight surrounding squares. At each timestep, the agents compare the amount of pheromone in the direction it is facing and the two neighboring squares. Then, it turns in that direction and might turn randomly, and then moves in that direction. After it is done, it leaves the maximum amount of pheromone on the square it is currently on. Then, the pheromone on each square is depleted by 1 unit, and then the next timestep starts.
The original idea came from https://www.youtube.com/watch?v=X-iSQQgOd1A&t=961s.
SI Table (per second)
31 August 2023
I recently made a table for all of the base SI units per second (to the power of 0, 1, 2, and 3). I got this inspiration from xkcd.com/2813/.
Binary Counting: on a Piano
1 August 2023
I was at Nueva Summer camp this week.
I had a class about fractals in that camp, and one thing the teacher showed was a puzzle video of him playing the piano. We were supposed to figure out what he was playing, and I got the answer pretty quick: he was counting in binary.
Example:
You probably have at least one of these questions right now:
Why is counting in binary related to fractals?
and
How do you count in binary on a piano?
MathPath Problem Solution
24 July 2023
Recently, my dad told me a problem from the MathPath qualifying quiz. I decided to write this on my blog to practice my teaching and writing skills. The problem goes: (summary)
- Let \(f(n)\) be a function that takes positive integers as inputs and also gives positive integers as outputs. We are interested in constructing a function with the following property: \(f(f(n)) = n + 5\) for every positive integer n. Is it possible for this function to exist? Prove that \(f(x)\) doesn’t exist or find a way to generate such a function.
3D Renderer Basics
7 July 2023
This week, I went to the Nueva summer camp. My morning class was game design, which used scratch. Scratch was already too simple for me, so I decided to try to one-up myself by attempting to create a 3D renderer, which I’ve never done successfully before.
In my past attempts, I searched up things randomly and tried to find something that would work. This time, I tried to think about it, and I came up with something really simple. I decided to make a youtube video about this, to try to educate people with not only the equations, but also how you get to that equation.
Link to the scratch project: https://scratch.mit.edu/projects/871926401/
MITM
2 July 2023
I recently went to Wyoming for the first time for a math camp (Math in the Mountains). Everything about this trip was good, except for the fact that there were bugs there and that I dropped my iPad, which we now need to repair.
On the first day, we went whitewater rafting as a community event. This actually did unify the community, and because of that, I can now officially say that I have drunk half-diluted “champagne”. It isn’t actually champagne, but just a bubbly part from after the rapids, where a bunch of air bubbles appear because air got trapped under the rapids. After that, we went “hiking” (more like walking) along the banks of the Snake river, where we did see snakes.
From the second day on, we actually started to do math. I had mathematics of fairness first, then problem solving and games, and finally, intro to number theory. Surprisingly, they were all in the same classroom, and taught by the same family.
I Made an Electromagnet
25 May 2023
Notes:
The thing that I tested it with was not a magnet. Ferromagnetic substances are things that are attracted to magnets; they are not magnets themselves.
The higher the amount of turns (times you wrapped the wire), the better. This is the reason electromagnet V1 didn’t work.
My Rubiks Cube Collection
22 April 2023
I made a channel. This is my first video about my rubiks cubes.
Non-contact Thermometers and Infrared Radiation
28 March 2023
I got this idea from looking at one of those fire warmers that restaurants use outside. I was wondering how hot the clear shell was and how hot the flame was. Then I wondered if a non-contact thermometer would measure the shell temperature or the fire temperature.
The thermometer is basically a camera with only one pixel sensitivity that only measures infrared. As an object gets hotter, it starts radiating more and more infrared waves. The thermometer uses the reading of its one pixel to give a temperature to the user. A laser thermometer actually also measures infrared, it just has a laser pointer to show youwhere the thermometer is measuring.
I always thought that infrared was the same as heat. Thinking about this, it obviously isn’t, as heat is molecular jiggling and infrared is less energetic light (light as in visible light, not the whole light spectrum). What infrared actually has to do with heat is not as related.
Lasers, Flashlights, and Eyes - Part 2
17 January 2023
More experiments:
The lasers and flashlights don’t have a standard distance, like the sun, so I’m just going to make increments on the distance.
General formula:
if pupil area is < beam spread area (still don’t know the terminology):
real power = \(\frac {pupil area}{π(\frac{distance(divergence rate)}{2})^2} * power\)
The fraction part of this formula is baiscally a ratio of how much power actually reaches your eyes.
else:
real power = power
Lasers, Flashlights, and Eyes - Part 1
15 January 2023
This is about the strength of lasers, flashlights, and the sun and their effects to your eyes.
Lasers, flashlights, and the sun are comparable to white surfaces and mirrors. They both reflect most of the light coming at them, but looking at a bright light shining at a white surface is definitely better than looking at a bright light through a mirror. This is because the white surface scatters light while a mirror doesn’t. The flashlight is like the white surface (because it has a wide spread) and the laser is like a mirror (and the sun is a really, really, really bright flashlight).
A Short Paragraph on Capillary Action
20 November 2022
Capillary action is when a liquid climbs up a narrow tube without external force. Only some liquids and some solids do this, and others do the opposite. This might seem like perpetual motion, but it does take energy away from the liquid.
A Buncha Questions and (hopefully) Answers About Fire
25 October 2022
It all started when my little sister asked, “How hot is the sun?” Then the conversation went into, “Why can you die of heat? Isn’t it just a bunch of molecular jiggling?”
Qs:
Then finally, the first question about actual fire came. It was, “Will your body actually burn when exposed to the sun?” This might feel or actually be obvious, but my thought process was that once all of the oxygen was used up, it would stop and you would just fall into the sun.
The next question I had after thinking about oxygen(from the body) and the sun was, “What if oxygen falls into the sun?”
After thinking through that, I had another question. The question was a pretty bad one, since I forgot about something obvious. The question was, “Why does hydrogen and oxygen alone burn?” (yeah.)
And then just now, “How many elements can be incorporated into fuel of some sort?” (clarification: the fuel has to burn. Uranium would not be a ‘fuel’.) (Also, I decided to incorporate the ‘oxygen’ part of fire as part of the ‘yes’ section.)
As:
Does Speed Affect the Amount of Rain on Your Rainshield?
30 September 2022
I did get this idea from looking at rain on the windshield.
For now, the angle of the windshield is 45˚. The blue box represents the area of the possible rain that could end up on the windshield in the alotted time. Also, assume the density of the rain is constant.
Why Windshield Wipers Look Misaligned
15 September 2022
I did get this idea from looking at the windshield wipers in the car. Later, while talking to my dad, he said that, to him, they didn’t look misaligned. This is my opinion on this topic.
Chicken Egg Argument
25 August 2022
I made an argument for the popular question, “Which came first? The chicken or the egg?”.