This vector field represents gravity. It affects which direction the gravity would be pulling depending on where you are in relation to the earth and other planetary objects nearby. I find it interesting that it shows how the small objects do have an effect even though they aren't as big. I think the position of planets and how every planetary object affects this position is very interesting. It is cool that we can use math to understand space better.
Here is the vector field of Xizang's wind. The wind in Xizang is really strong.
This is a vector showing the magnetic field of the sun. I thought it was really cool because we often think about how Earth's magnetic field is but I have never thought about the sun's. It looks similar to what Earth's looks like. I wonder if it is strong enough to have an impact on the sun, like how Earth's protects us from the solar winds, or if the other energy from the sun is too strong and negates it.
This is a vector field representing the direction of wind generated from Hurricane Katrina. I found this vector field interesting because I know that Hurricanes can cause extensive damage to coastal cities and I’m interested in how such strong power can be represented through the vector field.
This is a vector field representing the varied speeds of water flowing on the surface of a river. The red spots indicate that the magnitude of the vector is greater so water flows more quickly there. Blue signals a smaller magnitude and a slower speed of water flow. I find it interesting how as the water moves from left to right, the speed increases around the rock. This must mean a whirlpool/rapids situation occurs around the rock. This example of a vector field interests me because I am a coxswain and my role involves steering a boat, so I am fascinated by how the water runs underneath our boats and how water currents impact our speed. Looking at water from a mathematical perspective is really interesting.
Here is the topography and water vapor transport vector field for Tibet and adjacent regions during July (the summer monsoon season). Bold lines indicate the direction of water vapor transportation, and arrows show the local strength of the water flux. I find this vector field interesting because it represents how the summer monsoon season brings a humid climate, as represented by the arrows and bold lines.
A paper published in September advocated for the use of vector fields when displaying data that deals with trajectory. The paper argues that with the rapid growth of data from systems like GPS, mobile devices, and the Internet, being able to effectively display such data has become increasingly difficult. It uses the example of data from GPS devices of taxis in Beijing from January 24-31 2018, and constructs a vector field using "colors depict the magnitude of taxi density, vector flow direction demonstrates the direction of taxi travel vectors, and vector flow velocity and opacity indicate taxi speed." This method of presentation helps effectively depict the distribution and flow of taxis in Beijing during this time.
This vector field shows the velocities of the ocean. The color is used to represent the magnitude of the velocities. This vector field shows raw data of the velocities. I thought this was interesting because the data is able to be used to predict the tide at different times. This vector field shows the position of the velocities as well as the depth of the ocean and the actual vector arrows for each velocity.
This is a vector field that shows the functions notated as v.x = cos(sin(p.x)) and
v.y = sin(p.y). Where (p.x) and (p.y) are coordinates, and (v.x) and (v.y) is a velocity at point p. The color of the field changes depending on the angle. I saw this on a site I found called Field Play that randomly generates different vector fields. I think it's cool how you can play around with the number of particles and their fade out speed to see the field in different ways. I also thought it looked pretty.
These are two vector files representing the daily commuting data for individuals in London and Paris, with the color of the arrows representing the magnitude of the vector fields. These vector fields were designed as part of a large-scale study (from 2019) that sought to use vector fields to describe recurrent mobility in large cities. Such mathematical modeling has key applications with regards to urban planning and infrastructure, such as in planning transportation centers or even forecasting the spread of diseases. I found these two vector fields to be really interesting because I feel that vector fields are usually discussed within the context of things such as wind and water, and thus was surprised to see them applied in this context. I really appreciate the importance of this study and the significance of the potential applications of this research, and I think it demonstrates how much mathematical modeling can be used in a wide variety of real-world contexts.
This vector field represents the ocean wind velocity during Hurricane Ike. In addition to representing the ocean wind velocity using vectors, this map represents the velocity using color. Areas shaded dark blue indicate the regions with the lowest ocean wind velocity, and areas shaded pink indicate the regions with the highest ocean wind velocity. If you look closely, you will see that the vectors within the regions with colors associated with low ocean wind velocity are shorter than the vectors within the regions with colors associated with high ocean wind velocity. I found this vector field to be interesting because I live in an area which is both near a beach and stormy during the summers. It is interesting to see how storms, such as Hurricane Ike, affect coastal conditions.
This is a vector field showing wind speed and direction for the San Francisco Bay Area. The colors on the map represent the strength of the wind in knots, while the direction of the arrows represent the direction of the wind. I thought this graph was interesting because it helped me realize the most efficient way to display this information: you have to display 2 variables in a way that is clear, and the combination of arrow direction and color coding is one way to do that. I also think it's interesting that in general, the wind speeds get stronger as you go out towards the ocean, but remain in the same direction over the whole graph. I'm sure there is a meteorological reason why this is, but I'm not sure what it is.
This vector field shows the velocity of a river at different points on its surface. I chose this vector field because I thought it was cool to see how this concept can be applied to parts of nature - like flowing water. You can see on the figure how the water flows and collects around a rock.
These two vector fields show ocean surface currents in the Gulf of Mexico. The first shows currents at 0 m depth and the second at 100 m depth. The arrows point in the direction of motion and their length represents the speed at which the currents move. There is scale bar at the top left to give a sense of what 20 cm/s looks like. I think it is really interesting to see ocean currents displayed like this as it gives a clear sense of the patterns, speeds, and directions of movement. I also think it is interesting to compare the vector fields at different depths. At 100 m, I see a lot more circular motion of the water.
This vector field shows the current and wave patterns in the ocean. I wonder how this changes over time and with different weather patterns. I thought it was interesting in relation to high/low tide or thinking about predicting where things would be carried if they were swept up in the ocean. I wonder how they drew the vector field if the ocean is constantly in motion and at what point the data is from.
This is a vector field I found of the wind, showing their direction and magnitude over most of North America on Jan. 3, 1999. I remember learning about fronts and high and low pressure systems in 8th grade but it is interesting to see it portrayed in a more advanced form that I would not have understood back then. The white lines are isobars (lines of constant pressure) and the closer they are together the more windy it would be as there is a sharper slope between the pressure levels. Another thing that was interesting to me was that it is much windier around the great lakes and the midwest and I was wondering if that was a normal thing that the lakes may effect or simply the fronts at this time. Chicago is called the Windy City, is it due to its proximity to Lake Michigan?
