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mathematics

Horizon chart

Horizon chart is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Horizon chart rather than just read about it. In short: A horizon chart or horizon graph is a 2-dimensional data visualization displaying a quantitative data over a continuous interval, most commonly a time period. The horizon chart is valuable for enabling readers to identify trends and extreme values within large datasets.

Horizon chart — main illustration
Horizon chart — illustration

Key takeaways

  • Horizon chart belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Horizon chart to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Horizon chart from memory before moving on to harder problems.

Reference excerpt

A horizon chart or horizon graph is a 2-dimensional data visualization displaying a quantitative data over a continuous interval, most commonly a time period. The horizon chart is valuable for enabling readers to identify trends and extreme values within large datasets. Similar to sparklines and ridgeline plot, horizon chart may not be the most suitable visualization for precisely pinpointing specific values. Instead, its strength lies in providing an overview and highlighting patterns and outliers in the data.

History The technique of constructing the horizon chart from an area chart was first developed by Takafumi Saito et al. at the Tokyo University of Agriculture and Technology in 2005. This technique was referred to as two-tone pseudo coloring. Subsequently, Panopticon Software independently commercialized the procedure and referred to the resulting visualizations as horizon charts.

Overview

The horizon chart is a variation of the area chart. Having established a horizontal axis, negative values are mirrored over the horizontal axis, while positive values retain their position. As an alternative approach, rather than reflecting negative values, they can be shifted so that the smaller value aligns with the horizontal axis. Layers are formed by dividing the areas into equal horizontal intervals and overlaying the resulting bands. Color is an essential visual element in horizon charts. It serves to differentiate positive values from negative values, and its intensity corresponds to the magnitude of the values. Typically, the color of each area in the horizon chart is obtained by overlaying multiple transparent bands, with more intense colors indicating larger values and less intense colors representing smaller values. Horizon charts facilitate a reduction in vertical space, resulting in a more compact chart that resembles a heat map. This enables the consolidation of a substantial volume of data into a single visualization. The compact nature of the horizon chart enables easy comparison of different data series within a single visualization. It also lends itself well to the creation of small multiples, where multiple horizon charts can be displayed side by side to analyze and compare various datasets simultaneously. This compact design enhances the efficiency and effectiveness of data analysis and interpretation.

Chart construction

When creating a horizon chart, the selection of the origin for the vertical axis, which determines the placement of the horizontal axis, is crucial. In most cases, the origin is set to zero. However, this characteristic of the horizon chart can be leveraged to emphasize trends based on an arbitrary value. By selecting a different origin point, such as a specific threshold or benchmark, trends and comparisons can be highlighted in relation to that value. This flexibility allows for the visualization to be tailored to specific analytical needs or to draw attention to particular trends or deviations from a chosen reference point. Once the origin of the vertical axis is determined, the quantitative variable is assigned to the vertical axis, while the continuous variable is assigned to the horizontal axis. The band layering process in a horizon chart involves dividing the range of values for a dataset into equal horizontal intervals and overlaying these bands to create the final chart. This is the main feature of an horizon chart, enabling its compact visualization. The small size of the final visualization, allows the comparison of multiple sets of data in a given series. Regarding the color scheme in a horizon chart, it is common to utilize a diverging color scheme, like red and blue. Red is typically used to represent negative values or values with a negative meaning, while blue is employed to indicate positive values or values with a positive meaning. This color scheme helps visually distinguish between positive and negative values, aiding in the interpretation and understanding of the chart. In their 2005 article, Saito et al. proposed a different approach to color usage in horizon charts. They utilized the concept of discrete coloring, where the range of the function is divided into multiple sequential intervals, and a distinct color is assigned to each interval. This allows for the precise reading of values based on color. Unlike divergent colors (such as red and blue), the focus is on using a continuously changing scale of colors to represent the data accurately. By employing this method, the horizon chart enables readers to interpret specific values based on the assigned colors within the chart.

Implementation Horizon charts can be created using various open-source tools. These tools provide the necessary functionalities to generate horizon charts from data. Some popular open-source options for creating horizon charts include D3.js, R and RAWgraphs among others.

See also Data and information visualization Area chart

References

Further reading Tufte, Edward (1983). The Visual Display of Quantitative Information. Cheshire, Connecticut: Graphics Press. p. 13. ISBN 978-0-9613921-4-7

External links Flowingdata Datavis.blog

Illustrations

Horizon chart: This image is an example of a horizon chart, illustrating a series of 13 datasets spanning from 2010 to 2020.
This image is an example of a horizon chart, illustrating a series of 13 datasets spanning from 2010 to 2020.
Horizon chart: The figure illustrates the five steps involved in transforming an area chart into a horizon chart:A. Define a horizontal axis to differentiate positive values from negative values. B. Reflect negative values above the axis, using blue for positive values and red for negative values. C. Divide the graph into distinct bands. D. Adjust the opacity of the areas based on the number of subdivisions. E. Layer the obtained bands on top of each other to create the final horizon chart.
The figure illustrates the five steps involved in transforming an area chart into a horizon chart:A. Define a horizontal axis to differentiate positive values from negative values. B. Reflect negative values above the axis, using blue for positive values and red for negative values. C. Divide the graph into distinct bands. D. Adjust the opacity of the areas based on the number of subdivisions. E. Layer the obtained bands on top of each other to create the final horizon chart.
Horizon chart: Horizon chart displaying the difference between greenhouse gas emissions of some European country and the corresponding European average for each year, ranging from 2012 to 2021.[8]
Horizon chart displaying the difference between greenhouse gas emissions of some European country and the corresponding European average for each year, ranging from 2012 to 2021.[8]

Worked examples

Example 1 — a first encounter with Horizon chart

Start with the simplest possible case. Write down what Horizon chart claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Horizon chart before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Horizon chart ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Horizon chart

In research
Horizon chart appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Horizon chart in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Horizon chart is common in secondary-school and first-year university syllabi. It links to neighbouring topics Statistical charts and diagrams, so understanding it makes those chapters shorter.
In everyday life
Look for Horizon chart outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Horizon chart in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Horizon chart means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Horizon chart out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Horizon chart in simple terms?

A horizon chart or horizon graph is a 2-dimensional data visualization displaying a quantitative data over a continuous interval, most commonly a time period. The horizon chart is valuable for enabling readers to identify trends and extreme values within large datasets.

Why does Horizon chart matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Horizon chart?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Horizon chart.

Tags

  • Statistical charts and diagrams

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