This interactive map shows how population is distributed by latitude or longitude. It animates the creation of a bar graph by shifting population from its location on the map to aggregate population levels by latitude or longitude increments. Each “block” of the bar graph represents 1 million people. Population is highest in the northern hemisphere at 25-26 degrees North latitude and 77-78 degrees East Longitude.
It should be relatively explanatory. Press the “Aggregate Population by Latitude” button to make a plot of population by line of latitude (i.e. rows of the map).
Press the “Aggregate Population by Longitude” button to make a plot of population by line of longitude (i.e. columns of the map). To see the population distributed across the map, press the “Show Population Grid” button.
This map was inspired by some mapping work done by neilrkaye on twitter and reddit.
Data Sources and Tools:
This map projection is an equirectangular projection. Data on population density comes from NASA’s Socioeconomic Data and Applications Center (SEDAC) site and is displayed at the 1 degree resolution. This interactive visualization is made using the awesome leaflet.js javascript library.
California is one of the world’s largest economies (as measured by gross domestic product), currently ranking 5th in the world (if it were judged as it’s own country). This map divides the rest of the US economy into 6 more or less equal parts (each the size of California’s) and they are all within about 10% of each other.
Instructions:
You can hover over a state with your cursor to get more information about the GDP of that state and the group of states that equal California’s economy.
Gross domestic product is a measurement of the size of a region’s economy. It is the sum of gross value added from all entities in the region or state. It measures the monetary value of the goods produced and services provided in a year.
The main sectors of the California economy are agriculture, technology, tourism, media (movies and TV) and trade. Some of the world’s largest and most famous companies contribute to the California economy, like Apple, Google, Facebook, Disney, and Chevron.
Data and Tools:
Data for state level GDP is obtained from Wikipedia for the year 2017. The map data is processed in javascript and then plotted using the leaflet.js mapping library.
This interactive simulation estimates the value of the fundamental constant, pi (π), by drawing lots of random points to estimate the relative areas of a square and an inscribed circle.
Pi, (π), is used in a number of math equations related to circles, including calculating the area, circumference, etc. and is widely used in geometry, trigonometry and physics.
This app estimates the value of pi by comparing the area of a square and an inscribed circle. The areas are calculated by randomly placing dots into the square and then counting how many of them are also inside the circle. If you do this enough times, you will get a rough ratio of the relative areas of the two shapes. These points are plotted on the graph (red if the fall inside the circle and blue if the fall outside).
Also shown on the graph is the value of our estimate of pi as the simulation progresses, from a few points to many thousands, to millions of points. We can see that when we have only a few points, the value may not be very accurate but as the number of points increases the value of our estimate gets closer to the true value. Running the simulation will add and plot 1 million points. After the first 100 points are added, the rate at which points are added increases. You’ll notice this as the speed at which dots fills up the square increases and because the plot is shown with a logarithmic x-axis.
Here is the math:
Length of side of square: $2 \times r$
radius of circle: $r$
Area of square: $A_{square} = 4r^2$
Area of circle: $A_{circle} = \pi r^2$
The ratio of areas is $A_{circle}/A_{square} = \pi r^2 / 4r^2 = \pi / 4$
Solving for pi: $\pi = 4 \times A_{circle}/A_{square} \approx 4 \times N_{dots_{circle}}/N_{dots_{square}}$
So pi is estimated as 4 times the ratio of dots in the circle vs square
Tools:
This was programmed in javascript, canvas and plotted using the open source plotly javascript plotting library.
I recently taught my daughter how to solve the rubik’s cube using “the beginner method”. She’s getting decently fast, but when we watched some youtube videos about really fast speed cubers, we were blown away by how fast people can solve the cube. The world record time is under 4 seconds! I thought it’d be fun to document the progression of world records since the cube was introduced in 1980.
What was interesting in looking through the records are the strange events that people compete in and post amazing times in. Blindfolded! With Feet! One-handed! Feet or one-handed is at least in the realm of possibility, though it would slow down my already slow solves, but blindfolded is next-level stuff.
Hover over the different data series for the events to see the record-holder’s name, country, solve time and competition for each world record. You can also toggle the y-axis scale from linear to log scale in order to distinguish between the latest world records as they tend to converge and have very small changes.
Not sure if it’s motivating or discouraging to see these ridiculously fast solve times. Knowing that we’ll never be able to beat people who solve the cube blindfolded is a bit humbling.
Data and Tools:
Data was downloaded from cubecomps.com, a speed cubing website and the data was plotted using the open-sourced Plot.ly javascript engine.
This visualization is one of a series of visualizations that present US household spending data from the US Bureau of Labor Statistics. This one looks at the income of the household.
One of the key factors in financial health of an individual or household is making sure that household spending is equal to or below household income. If your spending is higher than income, you will be drawing down your savings (if you have any) or borrowing money. If your spending is lower than your income, you will presumably be saving money which can provide flexibility in the future, fund your retirement (maybe even early) and generally give you peace of mind.
I obtained data from the US Bureau of Labor Statistics (BLS), based upon a survey of consumer households and their spending habits. This data breaks down spending and income into many categories that are aggregated and plotted in a Sankey graph.
Instructions:
As stated before, one of the keys to financial security is spending less than your income. We can see that on average, those in the lowest quintiles may be borrowing or drawing down on savings to live their lifestyle, while those in the highest quintiles are saving money and contributing to wealth. This fairly high level of borrowing/drawing on savings from the lowest quintile households may be deceptive because it includes seniors who are drawing down savings that were built up specifically for this purpose, and college students who are borrowing to go to school. These groups generally don’t have significant incomes.
How does your overall spending compare with those in your income group? How about spending in individual categories like housing, vehicles, food, clothing, etc…?
Probably one of the best things you can do from a financial perspective is to go through your spending and understand where your money is going. These sankey diagrams are one way to do it and see it visually, but of course, you can just make a table or pie chart or whatever.
The main thing is to understand where your money is going. Once you’ve done this you can be more conscious of what you are spending your money on, and then decide if you are spending too much (or too little) in certain categories. Having context of what other people spend money on is helpful as well, and why it is useful to compare to these averages, even though the income level, regional cost of living, and household composition won’t look exactly the same as your household.
Here is more information about the Consumer Expenditure Surveys from the BLS website:
The Consumer Expenditure Surveys (CE) collect information from the US households and families on their spending habits (expenditures), income, and household characteristics. The strength of the surveys is that it allows data users to relate the expenditures and income of consumers to the characteristics of those consumers. The surveys consist of two components, a quarterly Interview Survey and a weekly Diary Survey, each with its own questionnaire and sample.
Data and Tools:
Data on consumer spending was obtained from the BLS Consumer Expenditure Surveys, and aggregation and calculations were done using javascript and code modified from the Sankeymatic plotting website. I aggregated many of the survey output categories so as to make the graph legible, otherwise there’d be 4x as many spending categories and all very small and difficult to read.
This updated visualization is a detailed look at the breakdown how taxes are applied to your income across each of the tax brackets. The previous version of this visualization was a Sankey graph and this new version combines the sankey view with a mekko (or marimekko) graph view. It should help you to better understand marginal and average tax rates. This tool only looks at US Federal Income taxes and ignores state, local and Social Security/Medicare taxes.
Both the sankey and mekko graphs help you easily the size each of these tax brackets and the fraction of income in that bracket that you can keep and the fraction going to taxes. Also shown is the split of the regular income vs capital gains and how capital gains is “stacked” on top of the regular income.
The mekko graph is a stacked horizontal bar graph where the height of each bar is proportional to the size of the tax bracket and the bar is split into two parts: a keep and a tax portion. This makes it clear the progressive nature of the tax code, initial tax brackets are taxed at the lowest amounts and as you fill up more tax brackets, the tax rate, and the amount of money you must give to the government, increases.
As seen with the marginal rates graph, there is a big difference in how regular income and capital gains are taxed. Capital gains are taxed at a lower rate and generally have larger bracket sizes. Generally, wealthier households earn a greater fraction of their income from capital gains and as a result of the lower tax rates on capital gains, these household pay a lower effective tax rate than those making an order of magnitude less in overall income.
Also shown is a summary bar graph that shows the split in your total income into a part that you keep and the other that owed to taxes, i.e. your average tax rate.
This is a written description of how to apply marginal tax rates. The income you have is split across various tax brackets, which by analogy can be thought of as buckets where once you fill one up, the additional money goes into another bucket, until that is filled up and so on until all your income is distributed across these brackets. The last brackets are open-ended so they are of infinite size.
You start with your deductions which changes based on your filing status, age and if you have itemized deductions. You fill this up first and you can think of this as the 0% tax bracket. Then any additional income goes into the 10% bracket where 10% of this income goes to taxes. This proceeds then onto the 12%, 22% and so on brackets.
The default example is described here for tax year 2025
This table lets you choose to view the thresholds for each income and capital gains tax bracket for the last few years. You can see that tax rates are much lower for capital gains in the table below than for regular income.
Data and Tools:
Tax brackets and rates were obtained from the IRS website and calculations were made using javascript, CSS and HTML. The sankey graph was made using code modified from the Sankeymatic plotting website and the mekko graph was made using the Plotly javascript open source library.
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