Convert pixel coordinate to complex number. Compute the number of iterations. The color depends on the number of iterations. Plot the point. Create your playground on Tech. This playground was created on Tech. Suggested playgrounds. How to build a chatbot in less than 50 lines of code.
Basic Image Manipulation. Basic Introduction to Recursion in Python. If it diverges within the the first few values of n currently set to 18 C is assumed to be already diverged and color's its pixel black. All other values of n are assigned a color using the "Color Scheme" menu. There are 3 absolute coloring schemes where the colors vary smoothly with n between 18 and maxit-1 using a particular spectrum Serene, Flamboyant and Goethe's Rainbow. There are two random schemes where the color values for each n beween 18 and maxit-1 are chosen at random from two different spectra Rainbow and Serene.
The default color scheme is "Repeated" where the colors from the Rainbow spectrum are recycled over a repeating range of n. This scheme was used to create a majority of the images in the Fractal Gallery. Here is an example. Figure 4. We can also make different images from the same iteration array by using different colorings.
For example, Figure 5 shows that "Flock of Owls" and "Racing Elephants" come from the same iteration array. Note: We don't distinguish two images if one is given by a rotation or a vertical or horizontal flipping of the other. Our coloring scheme has two parts: We first decompose the canvas R into a finite number of subareas and then paint each subarea by a single color like black or by a combination of gradual color changes such as from red to purple and from purple to blue as shown in the image of Figure 1 on the left.
The canvas for the Julia fractal of Example 1 has a natural decomposition into two subareas, A and its complement separated by the Julia set; see Step 2.
The decomposition may have just one subarea namely the canvas itself as is the case in "Racing Elephants" of Figure 5. Suppose A is a subarea of R and C 1 and C 2 are two distinct colors connected by the line segment 2. The color C assigned to d i , j by the function is the color we use to paint the pixel i , j in A.
Then set 3. Thus, 3. More generally, if f is any continuous function with the interval [0, 1] as its domain and range, then 3. Figure 6 shows six such functions including 3. The idea of functions and graphs belonging to precalculus works well here.
Applying the periodic coloring functions with an appropriate frequency of ups and downs on the subarea J in Example 1 , we get "Seahorse Couple" of Figure 7. We can find an appropriate frequency by rather instructive trial and error computer experiments.
Periodic Coloring Functions with Yellow and Brown In fact, the idea of the periodic coloring functions can be modified to involve more than two colors, Figure 8 shows two such examples. By the way, a seahorse is called "dragon's illegitimate child tatsu no otoshigo " in Japan.
Figure 9. The coordinate axes may not have the same scales. Imagine that we are shrunk to a pixel size in a fantasy land and walking around in a hilly area of the contour map F 3. The numbers denoted by D i a i, j and D j a i, j and computed by 5. Since we don't use the "normal" partial derivatives that can be approximated by formulas like 5.
Hence, the greater the partial derivative D i a i, j , the steeper the uphill. The same thing can be said about D j a i, j with respect to the south direction.
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