c and )
The instruction set is 32 bits in size. ( The TFT_eSPI library defines the connections in a setup file (attached) which must be put in the library's directory. {\displaystyle |z_{k}|} 465 322.5 384 636.5 500 277.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o
2 c In order to draw the Mandelbrot set and colour the domain outside it, we must have chosen a maximum iteration number M, a very small number
/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/exclam/quotedblright/numbersign/sterling/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/exclamdown/equal/questiondown/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/quotedblleft/bracketright/circumflex/dotaccent/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash/hungarumlaut/tilde/dieresis/suppress
k /
f {\displaystyle g'(z,c)=\partial g(z,c)/\partial {z}} z The 4th image is a Julia set obtained after selecting a coefficient value equal to 0.414 in abscissa and 0.09 in ordinate. 16 0 obj 777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8
c z {\displaystyle zc_{2}(c)}
f We start with the green palette. d z Clicking on the image zooms around the selected point.
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{\displaystyle f(z)+c} {\displaystyle zc_{2}} I hope you will enjoy playing with this program and that you will be able to display nice fractal pictures. endobj >> z >> 1
{\displaystyle g(z)=z^{4}-1} << But we can find interesting Mandelbrot sets by letting c enter in a specific way.
. . 30 0 obj ′ Different points correspond to different sets of Julia and depending on their behavior, we can decide to color the point in a particular way.
z (and critical point 0), we can find this motif in the Mandelbrot set (first picture): 2. d = 1 (m = n + 1). / 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 for k < M, we colour c according to k, or rather, the corresponding real iteration number, which is found in the same way as for a Fatou domain, by dividing k by r (and taking the integral part) and from this number subtract
{\displaystyle g(z)=f(z)+c} /Subtype/Type1 −
for the function | z
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323.4 877 538.7 538.7 877 843.3 798.6 815.5 860.1 767.9 737.1 883.9 843.3 412.7 583.3 f
/BaseFont/MOVWTL+CMMI10 + 593.7 500 562.5 1125 562.5 562.5 562.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
− (
,
The 3rd picture shows that computing times remain between 0.8 and 1.2 seconds for 320 x 240 pixels, which make it comfortable to zoom and display.
> N for k < M, we colour c according to k, or rather, the corresponding real iteration number, which is found in the same way as for a Fatou domain, by dividing k by r (and taking the integral part) and from this number subtract c k | (
272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 272 816 544 489.6
( 2 f 0 0 0 0 0 0 0 615.3 833.3 762.8 694.4 742.4 831.3 779.9 583.3 666.7 612.2 0 0 772.4 5 months ago
{\displaystyle f(z)+c} endobj
z
The usual Mandelbrot set consists of an infinite system of cardioids and circles, all lying outside each other and some touching. for the r points of the cycle. At the beginning of the 20th century, French mathematicians Pierre Fatou and Gaston Julia developed a sub-domain of maths called holomorphic dynamics. z c 2 {\displaystyle zc_{2}}
z
It reaches 3 seconds for 480 x 320 pixels, but provides more details. 1
{\displaystyle zc_{2}}
/Type/Font f Then a point in one of the holes inside the upper black. /Type/Encoding If z z 1 of the potential function of the Fatou domain for c containing
)
( {\displaystyle h_{2}(z)} {\displaystyle z^{2}} + z
( c
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