Fractals

My name is Ingvar Kullberg, born 1951, a dreamer, mainly interested on Mandelbrot and Julia fractals.

Most of the below pictures have been produced on my Macintosh, using Fractal Magic from Sintar Software. There Macintosh version is a commercial version of Dave Platt's MandelZot, an excellent freeware that can be downloaded from;

Of the 22 pictures, 20 comes from iteration of quadratic polynomials under the form: p(z) = z^2 + c with the critical point z = 0. The complex c is the parameter plane, and the Mandelbrot set is the set of all c for which the associated Julia sets are connected. The Mandelbrot set therefore sometimes is called quadratic connectedness locus. I have made 1280x960 resolution small prints (A4, 29.7x21 cm) printed on Canon CLC 800, CLC 1000, CLC 1100, CLC 3200, which I am selling in Sweden for 60:- including documentation in Swedish. To all of my pictures I have made customizised colour sets with the powerful editor in Dave Platt's program. Oh yeah, the newest ones are prodused with Ultra Fractal and fractal eXtreme with a resulution up to 12800x9600, that is 100 time resulution compared with the earlier ones! Here on the net the pictures are shown in 640x480 resolution. Click the picture to magnify.

Click the pictures to enlarge

	1) Spiraljuvel. Very deep zoom in #12, the Spiral of Peitgen.
	2) The Oval Fort. This motive is near #1.
	3) Cauliflower juvel. A very deep zoom in a secondary decoration joining the Elephants trunk in the aisle of the period 5 minibrot in the decoration emanating from the upper period 4 bulb.
	4) In the Centre of Chaos (ver 1). This the centre of a Julia set with a c-value from the region near #4. This motive occur in the parameter plane also (at the border of the Mandelbrot set) about two magnification step beyond the magnification limit settled by the precision of 19 digits
	5) In the Centre of Chaos (ver 2). Just another colour set than #5.
	6) Ice Queens in sunset. From a secondary decoration of the aisle of a minibrot, lying in a sceptre in the -1.25-valley.
	7) The Lotusfort of Seahorses. This is also the centre of a Julia set, made for the reason to lift forward structures in the Mandelbrot set beyond the magnification limit. The c-value is picked from a spiral in a Julia like structure in a secondary decoration in the Seahorse valley of a minibrot in a sceptre at the upper left side in the -1.25-valley.
	8) Flame among Ice Queens. From secondary decorations in the outer Seahorse valley of the same minibrot as in #6.
	9) The Pearl bracelet of the goody of Ice. A very deep zoom in secondary decorations in the aisle of the period 3 minibrot on the spike.
	10) Citadel in troubled water. From the same region as #10.
	11) The spiral of Peitgen. This is the famous spiral ending the seahorse tail at the period 29 bulb, occurring in the Beauty of Fractals, and some other publications. I've originally printed this motive in grey scale with the aid of Distance Estimating in a series of spiral motives (like #13, #14, #15) below.
	12) The scepter of Bishop Chaos. This 2-armed spiral originates from the period 28 bulb on the head-side of the Seahorse Valley (on the opposite side of "The Spiral of Peitgen")
	13) Chaotic eyes. The spiral is the period 67 elephant trunk deep in the aisle of the main Mandelbrot set. The full resolution picture is printed on Apple Laser Writer 4/600 PS of my own.
	14) Love shine several lights. A five armed spiral from the lower left period 5 bulb.
	15) Mothership Waiting. Deep magnification in the Seahorse Valley of the period 3 minibrot on the spike.
	16) Storm over the Tale Forest. Zoom in the hiearachy of the buds.
	17) The Pearl Palace of the Golden Land. Further magnification in the left flank of figure 15.
	18) Mandala Compass. Very deep furter magnification in the left upper corner of figure 15.
	19) Cauliflowerfort.Very deep furter magnification in the vincinity of motive #4.
	20) The infinity of the Blue Spirals.
	21) New! Octopus Mandala.
	22) New! The Hidden Treasure of the Marsh.

	23) Alien Forest.
	24) Sword of Joy.

Motives 1 - 22 comes from the quadratic space. Click here to see some magnifications of two dimensional slices from the four dimensional parameter space of Cubic polynominals.

Motive 23 - 24 comes from the Compass formula. More about this can be read in article 27) Compasses in my Chaotic series (see below)

Click the pictures to enlarge

3) Cauliflower juvel. A very deep zoom in a secondary decoration joining the Elephants trunk in the aisle of the period 5 minibrot in the decoration emanating from the upper period 4 bulb.

4) In the Centre of Chaos (ver 1). This the centre of a Julia set with a c-value from the region near #4. This motive occur in the parameter plane also (at the border of the Mandelbrot set) about two magnification step beyond the magnification limit settled by the precision of 19 digits

5) In the Centre of Chaos (ver 2). Just another colour set than #5.

6) Ice Queens in sunset. From a secondary decoration of the aisle of a minibrot, lying in a sceptre in the -1.25-valley.

8) Flame among Ice Queens. From secondary decorations in the outer Seahorse valley of the same minibrot as in #6.

9) The Pearl bracelet of the goody of Ice. A very deep zoom in secondary decorations in the aisle of the period 3 minibrot on the spike.

12) The scepter of Bishop Chaos. This 2-armed spiral originates from the period 28 bulb on the head-side of the Seahorse Valley (on the opposite side of "The Spiral of Peitgen")

13) Chaotic eyes. The spiral is the period 67 elephant trunk deep in the aisle of the main Mandelbrot set. The full resolution picture is printed on Apple Laser Writer 4/600 PS of my own.

14) Love shine several lights. A five armed spiral from the lower left period 5 bulb.

15) Mothership Waiting. Deep magnification in the Seahorse Valley of
the period 3 minibrot on the spike.

16) Storm over the Tale Forest. Zoom in the hiearachy of the buds.

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Click the pictures to enlarge

3) Cauliflower juvel. A very deep zoom in a secondary decoration joining the Elephants trunk in the aisle of the period 5 minibrot in the decoration emanating from the upper period 4 bulb.

4) In the Centre of Chaos (ver 1). This the centre of a Julia set with a c-value from the region near #4. This motive occur in the parameter plane also (at the border of the Mandelbrot set) about two magnification step beyond the magnification limit settled by the precision of 19 digits

5) In the Centre of Chaos (ver 2). Just another colour set than #5.

6) Ice Queens in sunset. From a secondary decoration of the aisle of a minibrot, lying in a sceptre in the -1.25-valley.

8) Flame among Ice Queens. From secondary decorations in the outer Seahorse valley of the same minibrot as in #6.

9) The Pearl bracelet of the goody of Ice. A very deep zoom in secondary decorations in the aisle of the period 3 minibrot on the spike.

12) The scepter of Bishop Chaos. This 2-armed spiral originates from the period 28 bulb on the head-side of the Seahorse Valley (on the opposite side of "The Spiral of Peitgen")

13) Chaotic eyes. The spiral is the period 67 elephant trunk deep in the aisle of the main Mandelbrot set. The full resolution picture is printed on Apple Laser Writer 4/600 PS of my own.

14) Love shine several lights. A five armed spiral from the lower left period 5 bulb.

15) Mothership Waiting. Deep magnification in the Seahorse Valley of the period 3 minibrot on the spike.

16) Storm over the Tale Forest. Zoom in the hiearachy of the buds.

Links

Thanks for visiting this homepage,,,Welcome back

15) Mothership Waiting. Deep magnification in the Seahorse Valley of
the period 3 minibrot on the spike.