Could we 'see' behavior of functions using color as the second dimension? Here, a few functions are plotted and the brightness or darkness of a corresponding horizontal position depends upon the function's output. Below, an entire family of functions.
The image below shows five functions, each a larger multiple of the next (starting at the bottom). Go to the jump to reveal which function.
By reflecting a function to fit within a particular domain, the result is what I'm calling laced-up functions (as if you were able to wrap the function around a particular width). Above is f(x) = sin(x) and below is a cubic, f(x) = x^3.
Above left is f(x) = x*sin(x) and above right is another cubic. Below is f(x) = x^2 and sqrt(x).
Above x+sin(x). Below 1/x and tan(x).
A few triangles and many quadrilaterals are drawn using spiraling points as vertices. The color is changed depending upon each polygon's position. Above, you can see the outlines of individual quadrilaterals. Below, every other polygon is drawn.
Each circle in the arrays is sensitive to a point in the geogebra file. The color/shading and the relative size changes as the distance to the point changes. The result is sort of a heat map with interesting patterns created in both the overlapping circles and the negative spaces.
Here Geogebra chooses random angles and lengths to provide data for segments originating from a single point. By connecting the midpoints, you create what I'm calling starburst polygons. Below is detail of a 100-sided polygon. Above, the three polygons' sides vary. Download the file and adjust the number of sides. Currently, the color of each polygon is a function of the first polygon's area.
Two sets of two sequences to create one set of closely-spaced circles and another of practically inseparable ones. If you choose to download the file, you can alter the amount of spacing, and, of course, the colors.
This visual demonstrates 100% interest compounded over different amounts of time. The larger (and lighter) the points, the shorter the intervals of compounding. The smallest points represent compounding one time, while the largest are compounded 200 times.
A sequence of overlapping circles following a sine curve.
This drawing attempts to build a tower of circles tangent to one another with the top circle adjusting to fit in the remaining gap between the tower and the top of the square.