We're now at 1,000,000,000× (billion times!) magnification deep in the neck of a small beetle that is out on the proboscis of the main beetle ⊕ 0.022141191996 +i0.652476712897 Here we dive into a filament on the head of beetle where we findĪ small beetle and dive into a filament on its body toll we get down toĪn even smaller beetle at 130,000,000× magnification. The very left tip of the beetle's proboscis in the negative real axis. Is embedded in a filament off the main beetle's hips ⊕ -1.99991175020Īnd now we are down at 130,000,000× magnification at This beetle in a radiating crown at 17,000,000× magnification Now we are at more than 8,000,000× magnificationĭeep in the anus of the main beetle, right along the real axis To reveal this interesting patchwork, and unusual asymmetric distorted beetle ⊕ 0.250006 magnified a bot more than 2,000,000× we have zoomed into aīeetle off the shoulder of the main beetle and then zoomed into the small beetle's anus Of the large beetle and then into a filament coming off one of the smallīeetles to get this filament which has an even smaller beetle embedded in ⊕ -0.48271895 +i0.53096651ĭeep in a cleft off the shoulder at 500,000× magnification is this highly textured structure. ⊕ -0.745263 -i0.113042Īnd even further up into the cleft between the head and body, zooming in a bit to 10,000× we find this beautifully symmetric pair of spirals around a beetle. Just off the buttox of the main beetle at 8,000× there is this square structure. Higher up on the shoulder at 8,000× magnification we find these two spirals trapping a beetle between them. ⊕ -0.658448 -i0.466852Īlso at 4,000× magnification, on the shoulder of the beetle is this Zooming in more to 4000× magnification deep in neck shows a kind of lacework alongside a spiral. This beautiful and delicate 1,000× magnified structure is in the neck (the gap between the main cardioid and the large circle). This is close by the above image at the same 1000× magnification, focussing on a spiral and a whirlpool. Here we looking at a 1,000× magnification of a swirling area on the positive real buttocks of the beetle, with many small beetles floating around. On a filament that extends upward in the positive imaginaryĭirection from the main cardioid. Here we zoom in 250× into a smaller copy of the beetle that's attached Images ⊕ 0Ī circular head with a proboscis. Out of these simple mathematical operations we get these incredibly complex and fascinating images. ⊕ For a detailed discussion of the algorithm see Hill-Shading the Mandelbrot Set This is done by considering that the colored bands to be contours on a mapĪnd shading it accordingly to show the slope. You will also notice a subtle shading which seems to show relief. The colored areas surrounding the black of the Mandelbrot set are values of c for which z eventually goes to infinity, with the colors indicating how many iterations until | z|>2 The black area is the Mandelbrot set itself, which are the values of the complex number c such that if you repeatedly iterate z ← z² + c starting at z=0 the value of | z| stays less than 2. These are images of the space of complex numbers. ⊕ For more background on my fascination with this set and the development of the software see Finding Mandelbrot images to use as video conference backgroundĬlick on any image to view a full-resolution version, suitable for exampleĪs a video conferencing background. This site is a showcase for Mandelbrot set images generated by the almondbread software. Exploring the Mandelbrot Set Exploring the Mandelbrot Set
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